So certainly not the "recommended" tactic, but I removed my Davis reflector and keep it in a locker. I don't think a reflector makes a difference with any radar sold in the past 10 years or so. A modern radar can see birds, rain, small wooden rowboats, and even some floating debris. In many conversations with both other sailors and with large ships, the Morgan has a very strong return without any reflector at all.
If you chance by a boat with a 30 year old vacuum tube type radar, they will need the reflector to be able to see us. It's pretty rare to see those, as the tubes need regular replacement, and mostly are not available anymore.