Hi D., (*welcome*)
Before a couple years ago, I never had a cat, only dogs. At my work, a "stray" adopted me, and he was so sweet, I couldn't stand to take him to the SPCA, so after my husband agreed, we brought him home.
Long story short: the little guy had his claws, and both my dogs are pretty gentle (lab-mutts), so I kind of just cut them loose together. I figured keeping them separated would increase all animal-anxiety in the house, and there'd be a big fight (or worse).
Don't get me wrong, I "supervised" the whole thing, and after 20 minutes, I separated them until the next day for another "session." I worked great!
The dogs were curious, but one "hit" from those claws was enough to keep them from over-doing it (he-he). Within a month, the younger dog was playing with the cat.
Good luck!
T