I think extending into the corner is better in this case, because I think white ends up too weak if he cuts. You seem to notice that yourself, which is good.
Here's a few tips on the plays in the diagrams you came up with.
$$W
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . O X . . . . . .
$$ | . . O X X . . . . . .
$$ | . 3 O O X . . . . . .
$$ | . 1 X X O O . . . . .
$$ | . 2 . X X O . 7 . . .
$$ | . . . . 6 4 5 . . . .
$$ | . . . . . . . . . . .
$$ ----------------------
- Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . O X . . . . . .
$$ | . . O X X . . . . . .
$$ | . 3 O O X . . . . . .
$$ | . 1 X X O O . . . . .
$$ | . 2 . X X O . 7 . . .
$$ | . . . . 6 4 5 . . . .
$$ | . . . . . . . . . . .
$$ ----------------------[/go]
This

gives white better eyeshape while protecting the cut, and also avoids forming an empty triangle.
$$W
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . O X . . . . . .
$$ | . . O X X . . . . . .
$$ | . 3 O O X . . . . . .
$$ | 8 1 X X O O . . . . .
$$ | . 2 . X X O . 7 . . .
$$ | . . . . 6 4 5 . . . .
$$ | . . . . . . . . . . .
$$ ----------------------
- Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . O X . . . . . .
$$ | . . O X X . . . . . .
$$ | . 3 O O X . . . . . .
$$ | 8 1 X X O O . . . . .
$$ | . 2 . X X O . 7 . . .
$$ | . . . . 6 4 5 . . . .
$$ | . . . . . . . . . . .
$$ ----------------------[/go]

is a small endgame move. It is worth only a couple of points. These moves shouldn't be played until the end of the game.
$$Bm8
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . 2 . . . . . . .
$$ | . 3 1 O X . . . . . .
$$ | . . O X X . . . . . .
$$ | . O O O X . . . . . .
$$ | . O X X O O . . . . .
$$ | . X . X X O . O . . .
$$ | . . . . X X O . . . .
$$ | . . . . . . . . . . .
$$ ----------------------
- Click Here To Show Diagram Code
[go]$$Bm8
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . 2 . . . . . . .
$$ | . 3 1 O X . . . . . .
$$ | . . O X X . . . . . .
$$ | . O O O X . . . . . .
$$ | . O X X O O . . . . .
$$ | . X . X X O . O . . .
$$ | . . . . X X O . . . .
$$ | . . . . . . . . . . .
$$ ----------------------[/go]
Instead, cutting white seems like a good move. If

, take your time to confirm that

captures the five white stones.
If white plays as below:
$$Bm8
$$ | . . . . . . . . . . .
$$ | . . 5 . . . . . . . .
$$ | . 4 3 . . . . . . . .
$$ | . 2 1 O X . . . . . .
$$ | 6 . O X X . . . . . .
$$ | . O O O X . . . . . .
$$ | b O X X O O . . . . .
$$ | 7 X . X X O . O . . .
$$ | . a c . X X O . . . .
$$ | . . . . . . . . . . .
$$ ----------------------
- Click Here To Show Diagram Code
[go]$$Bm8
$$ | . . . . . . . . . . .
$$ | . . 5 . . . . . . . .
$$ | . 4 3 . . . . . . . .
$$ | . 2 1 O X . . . . . .
$$ | 6 . O X X . . . . . .
$$ | . O O O X . . . . . .
$$ | b O X X O O . . . . .
$$ | 7 X . X X O . O . . .
$$ | . a c . X X O . . . .
$$ | . . . . . . . . . . .
$$ ----------------------[/go]
White has to
push along the second line twice before coming back with

to make two eyes. Black might now have to play

or 'b' (or the more simple but slightly worse for points 'c') to avoid a white play at 'a', which turns the situation into a rather complicated life and death situation which I don't think black can survive from.
$$W
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . O X . . . . . .
$$ | . . O X X . . . . . .
$$ | 9 3 O O X . . . . . .
$$ | 8 1 X X O O . . . . .
$$ | . 2 . X X O . 7 . . .
$$ | . . . . 6 4 5 . . . .
$$ | . . . . . . . . . . .
$$ ----------------------
- Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . O X . . . . . .
$$ | . . O X X . . . . . .
$$ | 9 3 O O X . . . . . .
$$ | 8 1 X X O O . . . . .
$$ | . 2 . X X O . 7 . . .
$$ | . . . . 6 4 5 . . . .
$$ | . . . . . . . . . . .
$$ ----------------------[/go]

is another endgame play and like before is too slow.
$$W
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . 9 . . . . . . .
$$ | . . 0 O B . . . . . .
$$ | . . O B B . . . . . .
$$ | . O O O B . . . . . .
$$ | X O X X O O . . . . .
$$ | . X . X X O . O . . .
$$ | . . . . X X O . . . .
$$ | . . . . . . . . . . .
$$ ----------------------
- Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . 9 . . . . . . .
$$ | . . 0 O B . . . . . .
$$ | . . O B B . . . . . .
$$ | . O O O B . . . . . .
$$ | X O X X O O . . . . .
$$ | . X . X X O . O . . .
$$ | . . . . X X O . . . .
$$ | . . . . . . . . . . .
$$ ----------------------[/go]

is a great point instead which gets
gets ahead in the pushing battle. This move is simply huge - it builds fourth line territory, protects your cut, and has a large effect on the center. Black's

stones go from looking strong to looking very weak with this one move. Speaking of the cut, if black plays

, you can probably see how to capture that stone. (Hint:
Click to show).
$$W
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . 0 . . . . . . .
$$ | . . . O X . . . . . .
$$ | . . O X 2 . . . . . .
$$ | . . 3 1 4 . . . . . .
$$ | . . 5 X 6 . . . . . .
$$ | . . . 7 8 . . . . . .
$$ | . . . 9 . . . . . . .
$$ | . . . . . . . . . . .
$$ ----------------------
- Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . 0 . . . . . . .
$$ | . . . O X . . . . . .
$$ | . . O X 2 . . . . . .
$$ | . . 3 1 4 . . . . . .
$$ | . . 5 X 6 . . . . . .
$$ | . . . 7 8 . . . . . .
$$ | . . . 9 . . . . . . .
$$ | . . . . . . . . . . .
$$ ----------------------[/go]
This diagram looks pretty realistic. I think black should play

next because the difference between white and black getting that point is huge in this variation as well.
As for the tiger's mouth variation, I think it should end up the same as the diagram above, just with

and

in swapped places.