In the days of DOS, it was actually common to just 'cd' to a program folder and run the main .exe file within. So yes, just running without installing should work.
Since your Windows is a 64-bit version, it can run 32-bit software but not pure DOS programs as they're written for 16-bit systems. (A 32-bit version of Windows can still deal with 16-bit emulation via NTVDM or "NT Virtual DOS Emulation".)
It would be helpful to know what exactly these two programs are, but lacking that knowledge I would recommend
DOSBox which is a complete "true DOS" emulator capable of running DOS software which Windows' command shell can't.
It's actually designed to emulate an entire DOS hardware platform and run classic games, but should serve your purpose too.
DOSBox, an x86 emulator with DOS