Geez, you just had to find a pair of speakers that are at the very top of the list for being a PIA to get into.
You may have to wait until it's dark, or find a dark room. Get a flashlight and look around the basket of the woofer, through the grill cloth. Look for the shiny screw heads that may or may not be around the woofer. Take your time, check and re-check.
If they're there, then it's easier to cut the grill cloth out (no grill frame on those). Once that's done, you can remove the woofer and easily replace the capacitors. Of course, you'd want to angle the razor, pull on the cloth a bit, so as to cut as much as the cloth you can. Then, hopefully, you can re-use the cloth and affix them to a new frame.
I have meat hooks for hands and I simply an unable to replace the capacitors through the cut-out in the back.
If you are sure that there are no screws holding the woofer in place, then you have a very early pair. There is no woofer basket/frame. The woofers are actually built-in to the front baffle or motor board. With these, you are forced to replace the caps from the hole in the back. Neat, eh? Let's just cross our fingers and hope that you find screws.
Biggles