You'll just be dropping the axle not the springs. I would try to have the TV connected just for stability. You'll still have wheels on the other axle. Once the axle is off I would check the equalizers, bushings, hangars and bolts.
As stated make sure you get the new one parallel to the old one. Make good tight electrical connections for the brakes. Torque don't guess and recheck them after towing.
When I replaced both of mine I also went the extra mile with everything new lug nuts, bearings, seals, hubs, brakes, brake backer plates. All the extras ran about $350 for both axles. I got these parts from a surplus RV store but I had no shipping with local pickup. I also replaced the equalizers, links and added never fail bushings after getting into the project. All new and good to go for years to come.