[EliotL]

Have you tried tapping with your existing phone?
This mimics pulse dialing, you just have to quickly tap the button on your phone that you use to hang up, tap once for 1, twice very quickly for 2, thrice for 3 and 10 for 0 etc... like you could try ringing the speaking clock on 123 by tapping to check if you have pulse dialing support!
I wouldn't try actually ringing someone like that as it takes ages and you have to try and tap 10 pulses per second!