Any advice for changing filter types in an aquarium?

I have a 2.5 gallon acrylic Hex tank with a male Betta and a mystery snail. The tank has been completely cycled for quite some time now. The tank came as a package (TopFin AquaScene 2) with an undergravel filter. The filter seems to be working ok, but I keep hearing so many negative things about UGF filters. Plus, there seems to be a lot of surfarce agitation from the air pump bubbles and my Betta can't create bubble nests. I would like to replace the UGF with a small 3 gallon in-tank filter that I have in a different 2.5 gallon tank.

Is it ok to change fitler types in a cycled tank? If I do, do I have to re-cycle the tank? Do I need to completely clean out the bottom of the tank, below the UGF plate? Or just remove the plate?…