Is there a way to use Picasa Web albums without having to use/share it on Google Plus?
Yes, you can use Picasa Web Albums without Google+.
Currently what happens is that when you try to go to Picasa Web Albums, you are redirected to Google+ Photos, but there you are given an option to go back to Picasa Web Albums:
Clicking on the link takes you here.
You can directly bookmark this link to directly goto Picasa Web Albums each time.