Yes, the press in zerks are available from a Cub Cadet dealer, and I think they are 1/4"
The front axle may be a bear to remove. You are suppose to be able to do as you say and drive the spriol pin out, then drive the axle pin out , usually back to front. That will work if the front axle has a grease zerk in it (usually in the webarea of the casting) to allow that pin to be greased. The early model Cub Cadets did not have a zerk and the pin and axle would rust together. That would then break the spriol pin, and the axle pin/axle would then turn/pivot in the bushings of the crossmember. If that has happened, the only way to remove it is to cut the axle pin on both sides of the axle with a sawsall/reciprocating saw to remove the axle, and then drill the remaining pin out of the axle....or replace the axle with another. It is nearly, if not, impossible to press that remaining piece of the pin out of the axle, without damage. If it does come out you will probably have a heartattack when it "pops", and think you have been shot with a g-r-e-a-t b-i-g gun.
The axle may have been retrofitted with a zerk, so check all around the pin area for one, and hope it was used for its intended purpose. Make sure what ever axle to put back in the tractor has a zerk installed