Yes, this will fit the Walther CCP.
No, it will not...unless you're willing to do some shaving with a knife. I bought a Walther CCP .380 for my daughter and bought the TLR-8 solely because of the answer given to your question. I tried every combination for the spacers provided, turning them every which way, and none of them worked.
Be wary. We did in fact install this on her CCP and it seemed to fit like a glove until she started shooting and the TLR8 began sliding forward. That's when I noticed she had the wrong spacer installed (or so I thought). I found one spacer manageable enough to do some "meaningful" shaving with a knife without compromising the integrity of the installation.