No the epoxy won't hurt at all, just use a very thin line along the edges of the tailwheel assembly, and do NOT use the epoxy alone and count on it holding the assembly in place for long (maybe only a landing or two before it breaks off). Use a line of epoxy along the edges where it meets the fuselage only AFTER screwing the tailwheel base in place with no less than 3 #4X3/4 screws. You can even apply a dab of epoxy into each screw hole before installing the screws. Wipe off any epoxy that oozes out around the screws with a cloth and rubbing alcohol.

Let us know how it comes out.