Is this a job
for a do-it-yourselfer (considering the need to recharge the freon,
etc.)?

I'm pretty handy, but I would pay someone to change & recharge a
refrigerator compressor. The lines must be silver soldered in, they
seldom have valves installed, so that must be done as well. To do that
properly, you need a torch set, a vacuum pump, a set of gauges, freon
(which is getting a little hard to come by) and to do it legally, a
license.