If you don’t want to damage the roof as bad, I have anchored a 2x4 rail and then I would run solid or flex ducting along that. A pack of cheap ratchet straps, screws and washers, cut the straps to length.
They make nylon strapping material for hanging ducts specifically. I've used that and just put a screw/washer to side walls. For hanging you'd want some type of hardware that is intended for vertical loads. Plant hangers for instance. If you don't want several holes do like suggested above and make 1 primary rail anchored well and then staple or otherwise attach the straps.
Find the Master Flow 1-3/4 in. W x 3600 in. L Woven Vinyl Hanger Straps (12-Pack) HS1.75WV, cut to size hang insulated or regular duct work or round pipe to prevent sagging over long runs from The Home
If wood frame construction, just put some eye/hook screws into the wood joists (not just the sheetrock/drywall). Then use above strap, or some zip ties or small bungees to hang the duct. That's what I did. My $0.02.
I use the black fabric strap above and a screw, for the ducting. For the filter and fan I use big ass eye hooks and ratchet straps like you would use for a motorcycle or something you were hauling.