With the axle out, it will aid the process of removing the oil filter housing and replacing the gasket from housing to block. The two housing to oil cooler o-rings are best replaced via removing the cooler/heat exchanger from the filter housing through the passenger wheel well, so the axle being removed has no bearing on that.

FYI, if you’re replacing the axle, you might want to also replace the output shaft seal while you have it out.

It’s the “output” shaft seal, where the inboard splined end of the axle goes into the gearbox, and no, it’s not particularly difficult to replace. Just need a longish thin flathead screwdriver or prying tool to carefully pry it out. Old seals can be inflexible, and require a little more effort to get out.

Clean orifice well after seal has been removed.

New seal is lightly lubricated before being tapped evenly back into place and you’re done.