I don't think you'll be able to mess up plain old remote keys with the magnet. No idea about the new fancy chip ones, cause I have no idea how those work.
But quick physics lesson. It is unlikely you will break your keys by generating a sufficiently large change in magnetic flux to induce a current in your remote that destroys the wiring. Especially just by putting them there and taking them away. I think, anyway. Maybe it affects other components of the key thing, but you probably won't kill the remote like that.
Also I haven't been to ikea in a long time. But if their furniture is not super high quality, I bet some diy shenanigans could make it stay together forever.