Removing silicon caulk?

[gfw]

Not sure if this is a plumbing question, a flooring question or what, but it's definitely a bathroom question.

I've torn out the old vinyl on particle board floor in a bathroom and am laying a plywood underlayment for Marmoleum. Some of the old silicon caulk is still adhering to the side of the bathtub where the vinyl was sealed to it with said caulk.
1. Do I need to get every last bit of it off, or can the new caulk go over very small bits of old caulk?
2. Is there some sort of solvent I should use? I've been scraping it with a putty knive and I can get most of it, but there's still a bit of residue.

If you want to know what the tub is made from ... it looks like (white) enamel, feels slightly cold, like metal, but is non-magnetic.

Thanks!

 

[user 4883]

A one-side razor blade should get you down to where you need to be.

 

[gfw]

Thanks for that suggestion. I had thought a razor blade might scratch, but that surface is tough. It turns out I have a set of Exacto knives, and one blade is a "push" flat style. So I used that and it was great!