Should I set "the search path" to /usr/local/openssl/bin too or just
cp /usr/local/ssl/bin/openssl /usr/bin/
I guess you mean /usr/local/open
ssl/bin/openssl, as you've installed it under /usr/local/openssl/
Anyway, it's better to use a symlink, so if you upgrade your openssl installation, you don't have to remember to copy the binary again.
ln -s /usr/local/openssl/bin/openssl /usr/bin
Or you can add /usr/local/openssl/bin in the PATH env. variable.