I generally turn mine on before the board is turned on and then off before the board is shutdown. I’ve never had a problem in that order. I believe most, if not all, of the audio racks have fans so you would probably extend life by shutting them down when not in use. Mine are going on over 11 years old and are shut down at the end of the day and turned back on the next time we need them. Mine are powered on/off by a power sequencer installed in our AMP rack (with a hard wired remote switch).
However, there are plenty of cheap remote controlled power outlets online at stores like Amazon. I’ve used the Loratap remote controlled outlets for a ton of random purposes and I think they’d be good for your purpose. You can configure many remote outlets to work with one switch and vice versa. Just make sure you get one that supports the max current flow you expect through that circuit.
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