if you have spiders in your studio, it means you have various other critters as well.
Spiders are predators and would not be there if there was nothing (nobody) to eat.
In fact, the spiders are probably keeping your bug population down. Spiders are good. (Unless you have an easily creeped out female vocalist for a client.)
Get rid of the other bugs and the spiders will leave. This may involve spraying or dusting, but could also be a matter of sealing the place and making sure you don't leave food around that attracts the prey species.