Testing speaker capacitors

I am assumimg you have a pair of speakers? Just remove both tweeters and swap them. If the twetter works in the other cabinet, then you have a crossover, (or wiring) problem. If it doesn't work, you need a new tweeter.

Just take the tweeter out and touch the speaker wires to it playing something at low volume. It is most likely the tweeter and not in the crossover though. You need a capacitance meter to check the capacitors.

Caps can be checked using a DVM and the 'kick' test. Won't give an actual value, but at least that it is still a cap.
One leg of the part under test must be lifted.

The tweeter connection is covered with hard wax or plastic at the terminal box. How do I remove the hard stuff to disconnect the tweeter?

You really don't have to disconnect the tweeter to test it if you can get to it's terminals.

I want to switch L/R tweeters so I have to disconnect the bad one and connection is covered in hardened plastic.

It's probably hot glue.

You can use a hot knife, heat gun, or denatured alcohol to remove it.

Why go to the trouble to remove both tweeters just to check one? If you can't check the suspected bad one in it's cabinet, why not just remove it and touch the speaker wires to the terminals and play music through it at low volume?