I would probably buy or build an algae turf scrubber in your case before I turned that reactor into a refugium. If you still want a fuge, that's great - heck, I turned mine into basically a whole extra tank of its own - but a fuge and an algae scrubber are not really the same tool.
A refugium is great for biodiversity, pod production, overall system stability, and some nutrient export. What it
isn't is a fast answer to an established hair algae problem. Even good macro grows slower than nuisance algae a lot of the time, and it really starts working best once you already have enough healthy macro mass to compete.
So yes, you can convert a media reactor into a chaeto reactor, and yes, cheap LEDs can grow algae. But on a 90 gallon system, I honestly think that is likely to be more compromise than solution. You are limited on macro volume, limited on light penetration, limited on flow pattern, and it can easily become a detritus trap. By the time you rig a decent light around it, shield the spill, and still keep running carbon somewhere else, you may find you spent effort and money for a result that is just kind of... okay. There's a reason that neither refugiums nor turf scrubbers are sold commercially in that form-factor, despite the potential savings with COTS components: because it's just not well suited to it.
If your real goal is
hair algae control, I would lean towards an ATS first, as it's really the more direct tool for that job. If you want a refugium because you like the ecological benefits, pod habitat, and general system support, then I would build a real one rather than forcing the reactor to do a job it is not ideal for. Both can be done at the same time, but then have to be handled a bit differently re: lighting schedules and whatnot.
And if the algae is already pretty established, I would also add more actual grazers before expecting any reactor or fuge to save the day. In a tank your size, a pair of tuxedo urchins and a 8 - 10 trochus snails will usually do more immediate visible work than a little reactor fuge ever would, especially if you manually knock the worst of it back first so they are not starting against a full-grown forest. If for whatever reason inverts aren't an option, then DEFINITELY go with an ATS first: you can find all kinds of DIY instructions out there, if you want to go that route, but, don't use cheap lights if you want the result you're hoping for.
