The simplest way of achieving what you want is to use a telnet package which includes a script language.

There are dozens of commercial offerings, or you could try IVT which is freeware and includes scripting.

You will be able to create a script to log in to each of your switches in turn using send/wait semantics and either record the session to a file, or simulate screen prints to a file.

It also happens to be an excellent vt220 emulator.