Try specifying the password in your .protect line.

Thanks for your reply, David. I'm not sure how to do this (ie. VBA code) or
if this would produce the desired result: for the"Unprotect Sheet" password
prompt (with OK or Cancel as only options) to *not* appear when the users
open the workbook containing password-protected worksheets.

I may be misunderstanding the effect of putting the password in the .protect
line, however.