I've got the type two to 3 pin adaptor, it seems to work fine on public charger but a word of warning they can become stuck. This is because the Twizy is a 'dumb' electric car and can't tell the charger that it's finished.
Another point to make, ensure that the charge point isn't tethered! If you use an adaptor it must be a 'female' untethered point so you can use your adaptor.
If you must use a public charger, find one which uses a RFID card to disengage the charge. I use the local EV Driver network here in Suffolk, works a charm. I use my RFID card to engage the charge then tap again when I'm finished.
For transparency I have used Polar once when I was in a real pickle I used the app to start and end the charge and it seemed to work fine but I wouldn't use it frequently.