Hand-held DTMF tone generators, for exactly this purpose, were once fairly widespread. A financial institution once sent one to me for navigating its dial-up automated teller system.
Yeah, i looked for something like that to keep next to the phone but couldn't find anything. I was sure they used to be a thing. What you _can_ get however are little kits you wire up inside the pulse dial phone which do an on the fly pulse to DTMF conversion.
I had one early century about the size of a car key. Googling for something similar now I find nothing. Not necessarily weird given the current state of telephony, but kind of a bummer.
[0] https://en.wikipedia.org/wiki/Blue_box