On the driver's side there is no snap ring, the axle is held in by the bracket that bolts to the block.
To remove the axle seal, use a seal puller. You place it in behind the seal and pry it out.
KD Tools (KD 3245) Seal Puller - KD 3245
You can even use a hammer and a screwdriver to crush the edges of the seal in without damaging the transmission case, then pull the seal out with a pliers.
I personally like the jaw type puller. It works very well, and you can use it for other jobs too.
Reversible Jaw Slide Hammer Puller
Any of these methods should work for removal. When you go to install the new seal you must match the tool you are going to use with the outer edge of the seal to drive it in. Wipe some grease on the inside of the seal to help hold the small spring in place while you are seating the seal. It makes it much harder to knock out the spring this way.