Norcal, while your axle component arrangement is a bit different than the one shown in Kharman's thread about his TC40D, it also has to be removed so that you can get to the lockring clip behind the large final gear. In your tractor, you have a locknut on the end of the axle shaft that is not on the TC40D. I believe that will allow you to remove the axle without having to use a bearing puller, but you might need the puller for the inside bearing behind the final gear and lockring clip. I'm also pretty sure that you will find you need a special tool to drive the new seal into the seal retainer. If you are skilled, you can probably make one, but don't try to install the seal without some kind of tool that will drive it without deforming it.
EDIT: I would not want to do this job without a manual. It's not as complex as working on the differential, but there are lots of careful steps given in the Repair Manual that you might miss otherwise. I also think you'll need a transmission jack or other suitable adjustable platform to comfortably remove the rear axle housing. A floor jack might be sufficient.