I just went thru the identical same thing. There is a small spring clip that comes off inside the trans. I bought the clip and the axel seal fore under $10, a gallon of 20w50 sys oil and a tube of oil resistant RTV. Under$35 total. Trans came rite out, just shoot pics of the linkage bar connections. No need to remove the fan, belt goes rite over the top. When you open the trans, you'll see gears. One that went one the axel and the two it turns. I found my clip rite under the axel gear.
Now the hardest part, getting the wheel off the axel before you reassemble it. Lots of penitrating oil and time. If you're going to beat on the axel, make sure you don't mushroom either end. I have a hole drilled thru my work bench that I put the axel thru, and using a piece of rerod slightly smaller than the axel, I carefully beat it out. To reassemble, I installed and lube the new seal, slid the lubricated axel thru it, slid on the wnew gear and fought to get the spring clip on. I used needle nose plyers to spread it open and slide it on. Clean the trans case sides very well, apply the RTV and bolt it to torque specs. I refilled the oil while off as getting to the fill plug while in the mower is pretty hard. Install the trans back in, reconnect all linkages and belt and purge the trans.
Mine is running fantastic. Luckily, the other wheel came off easily. I got this mower cheap cuz the guy could not install the inner tube. Well worth the time and experience.