Is there some simple way to upgrade an existing flashlight to accept wireless input without spending almost as much as a new light?
I have many old but serviceable units I would like to use in a studio setting but no way to control them.
Depends on your definitions of "input" and "control." Knowing which "old but serviceable units" we're talking about would help us advise you a lot. From your thread title, you mean speedlights (battery powered hotshoe flashes), yes? Not plug-in studio strobes?
You
can add an optical or radio trigger to most speedlights: connecting them either on the flash's foot, or cabled to the speedlight's sync port (if it has one). But there are exceptions (Canon EX speedlights, for example, don't work in concert with most add-on optical slaves, like the Wein peanut).
And, unless the speedlights are digital-era TTL, and you're using add-on radio triggers that can communicate TTL, then the chances of having any "control" over the speedlight, other than firing it in sync with the camera shutter, is unlikely. (No TTL, HSS, power control, settings control, zoom control, etc.) So, the speedlight, to be useful in use off-camera, needs to have M mode, and a physical control (dial, buttons) to set the output power level. So, something like a Canon 420EX or Nikon SB-400, which can only have its power set from the camera when used on the hotshoe, isn't great for this kind of use.
Today, also, there are speedlights designed to be used off-camera that don't actually cost a lot. Something like a Godox TT600 is only $65. It has a built-in radio transceiver, so unlike an older speedlight with an add-on radio trigger, not only do you not need to attach a radio receiver to the flash, you can also have remote power control and HSS via an X1T or Xpro transmitter.
Given that radio/optical triggers themselves may already cost $15-40 apiece, and you might need to add on a $20 hotshoe-to-sync adapter, you may want to consider whether or not the additional cost of a new speedlight might not be worth it for the added convenience.