I don't have the Homedics programmable, but I have taken apart my Brookstone programmable (and lots of old Homedics massagers).

I'm going to guess the screws concealment method is similar. On the under side of the massager, look for small oval-shaped outlines that are the same color as the rest of the body. Mine had four. These are little plastic plugs that you can pry out with a tiny flat screwdriver or a razor blade. The screws are hidden under these plastic plugs.

I hope this helps

HoMedics PA-4H has 5 Phillips screws on the head and 2 Phillips screws on the handle.
The handle has a rubber grip that covers one screw, you can take the rubber grip off by sliding it towards the power cord (with a little force and some patience).
Once all 7 screws are out, unscrew the two plastic vibrating "heads" then gently open the housing.
You will need a soldering iron to unsolder the power cord from the pcb.
Hope this helps. Good luck.