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.
Woven Vinyl Hanger Straps are used to hang insulated flexible duct, round pipe or rectangular duct. This helps prevent the duct system from sagging over long runs.
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.