Unless you build statically linked versions it should be enough to just install a patched openssl shared library (libssl.so, libcrypto.so). If you are not sure you might check with strace on linux, e.g.:

 $ strace -e open perl -MNet::SSLeay
 ....
 open("/lib/x86_64-linux-gnu/libssl.so.1.0.0", O_RDONLY|O_CLOEXEC) = 3
+                                                                     
+                                                    
 open("/lib/x86_64-linux-gnu/libcrypto.so.1.0.0", O_RDONLY|O_CLOEXEC) 
+= 3
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If you see these libs loaded dynamically all is fine and you just need to replace them by installing the updated libssl package.