So I am thinking to use middle path: Template for HTML part of it,

That sounds like a sensible compromise. With the templates stored in external files this would make any later move to some other architecture less problematic too.

and I was advised to use PSGI in CGI mode for interacting with Apache instead of using CGI.pm.

You can do this but be warned that it increases the start-up time of the CGI scripts substantially. In my own tests of this the run time of a trivial script increased by a factor of 5 or 6. If that's OK in your scenario then it might be worth doing, again with one eye on the future.