Some older drives require different jumper setting to work as a slave. i.e. slave with master present, slave with cdrom drive, slave with no present. Some, as you say, will not work as slave and either have no jumpers or will not work with another hard drive, just a cdrom in which they must be master.
So if you take it that the drive will NOT work as a slave. All you need to do is to disconnect the IDE ribbon cable from your secondary IDE channel. i.e. the optical drives. Ease out the wide grey ribbon cable from both drives, if there is two, so both connecters are free. Connect one to the hard drive and then the power connecter.
Boot the computer and transfer the files.
" Would I then be able to run win 3.11 from the USB stick ? "
Only if you have the original disks and if the computer supports booting from a usb device.
If you are thinking of just dragging windows off the drive and booting from that, then no.
It might work if you can clone the whole windows 3.11 drive onto the usb stick.