I salvaged the mondo squirrel cage fan out of my attic air handler when I had my central HVAC replaced, with the intention of making a fume extractor. I haven't used it yet so I can't say how well it works, but I imagine it moves at least 400cfm.
But before I got that, my plan was to use an electric leaf blower. I did that before for some purpose I can't remember, but it worked well, whatever it was. I think it was... maybe, the dust evacuation for my DIY sandblasting cabinet? IDK but I made some sort of shroud/flange to couple a pipe to the intake of the leaf blower, and then powered it from harbor freight's "
router speed controller" (very handy, get one, I put that ship on everything) for variable speed/suction.
The leaf blower was a $30 job from home depot. Coincidentally, I just found that HF has a
leaf blower for $39 with, wait for it...
suction mode! Eureka! 375CFM, 230MPH, should evacuate a small weld envelope lickety split. Coupled with the router speed control you should be able to dial it in so that it doesnt pump all your heated air to the outside.
The only drawback I remember is that it's loud. Really loud. Like nearly as loud as ... a leaf blower. But dang effective. It's a bit quieter with pipes on both intake and outlet, and with it turned down by the speed control, but still loud. That's what left me with the desire to find something else and I saved the squirrel cage. But if your budget is $200 I think this gets you there with bucks to spare.
Note: that router speed control works for
brushed ("universal") motors. Routers, leaf blowers, shop vacs, blenders, (some) washer/dryer motors, (some) cheap compressor motors, corded drills, corded angle grinders, corded circular saws, etc. Will NOT work for induction motors like that duct fan, my squirrel cage fan, any decent compressor, etc.