If it is not possible with Midnight Commander, is there another easy way to copy and paste specific text from different files?
I, as author of putty4far2l putty fork, suggest you to try «far2l + putty4far2l» for similar to «mc + putty» user expirience, but with full clipboard support via commonly used Shift/Ctrl+Ins/Del and Ctrl+C/V/X key combinations. This software pair allows two clipboard modes: isolated, then your host and remote server uses different clipboards, and synced, then the same clipboard is used. You will be asked to choose on first clipboard access.
PS: ppa for far2l is here, putty4far2l's binary is available directly on github