
Star Trek historically handles this very well. Watch any episode of TNG where Geordi La Forge and Wesley Crusher have to solve some technical problem.
Medicine or goldsmithing or anything else like that don't have to work like they do in the real world, because FF is significantly different. Magic suffuses everything. So you can start in on the handwavium and merely make it look promising and come off as a genius:
"It appears to be magnetically sealed. ...I believe I can reverse the polarity by attenuating the aetheric servo..."
Medicine or goldsmithing or anything else like that don't have to work like they do in the real world, because FF is significantly different. Magic suffuses everything. So you can start in on the handwavium and merely make it look promising and come off as a genius:
"It appears to be magnetically sealed. ...I believe I can reverse the polarity by attenuating the aetheric servo..."