If you want to install the certificate in Windows you will ALWAYS get a popup asking the user for permission, unless the certificate comes from a root that is already trusted. If you don't want that the only option is to use the PFX contents from a memo field each time you need the certificate.
I have no experience with Capicom, but from what I read it is a Microsoft DLL that you use?
If you are having problems with Capicom and LibEay32 you might want to check out the Eldos Secure BlackBox components. I have very good experiences with those and their support is great.