The "best" solutions would imply modifying the server and or Windows box to make this easier (so you can use scp, ftp, SAMBA/Windows File sharing, NFS or similar).
As it sounds like none of those might be options, the easiest way may be to start a log file on the terminal emulator, cat the file, capture the output and then close the log file - editing out the bit at the top (and maybe bottom) showing the commands manually afterwards.
I've never used a wyse50 terminal, but was around in the "BBS" days (prior to the wide use of the Internet), and the standard way to do what you are trying to do would be to install a program like "zmodem" on the server (alternatives include "xmodem","kermit","bimodem" among others, but "zmodem is where I would start because it was simple and ubiquitous") and ensure the terminal emulator had support for it, then issue a command to send the program with xmodem and it would be capured to your system. I'd be willing to bet this could be made to work if your terminal emulator supports it - and most will. (Try using the program "sz" to initiate a transfer)