|No such thing as a small change|
The following should be all that's needed:
Neither Net::SSLeay nor IO::Socket::SSL need to find the openssl executable (or any config file) as they don't use it. Instead, Net::SSLeay uses the openssl library - which needs to be found when building that module from source.
If the openssl libraries against which it is built are dynamic ones (dll) then those dll files need also to be in the path whenever Net::SSLeay is used by a script.
(IO::Socket::SSL is just a pure perl module that uses Net::SSLeay.)
The above ppm package for Net::SSLeay was built against static openssl libraries - it doesn't need to find any openssl library at runtime, and should work fine even if there's no openssl installation on the PC, because the requisite openssl functionality has been built into that Net::SSLeay package. (Any existing openssl library won't do any harm - it just won't be used.)
I notice that those ppm packages for Net::SSLeay and IO::Socket::SSL are not quite current - I'll update them in the next hour or so, though I expect that the versions presently available would be suitable for your purposes.
Note that there are probably ppm packages on offer at other repos - some of those might require the installation of openssl dll files (which they should install for you).
UPDATE: Uploaded ppm packages for Net-SSLeay-1.49, but have left IO-Socket-SSL at version 1.76. The tests for IO-S-SSL-1.76 work fine against Net-SSLeay-1.49 (and 1.48), but t/acceptSSL-timeout.t (which hasn't changed from IO-S-SSL-1.76 to IO-S-SSL-1.79) hangs with IO-S-SSL-1.79. IO-Socket-SSL is pure perl, and easy to update if the OP wants.
UPDATE 2: The problem with IO-Socket-SSL-1.79 is fixed in version 1.80. IO-Socket-SSL-1.80 has therefore now been uploaded to the sisyphusion ppm repo.