Just went through the same thing last month. I shook them out on the ground and they drifted into the strong hive.
No worry about spreading any disease from wax moths. I removed all the frames and cut out the really bad ones and froze the frames that weren't all that bad.
The wax moths will not bother your strong hive. The moths are always around bee hives but the strong hive will stay on top of removing them.
They only get out of control in the weak hives.
I also would air out all your equipment, hive stands, bottom boards, supers, etc. in the sun. The sun and air kills the wax moths.
Hope this helps