Mobility scooters do not need to be registered like motor vehicles do.
You can usually legally ride your mobility scooter down the road even without needing to register it as long as you're driving the mobility scooter down the road safely.
Mobility scooters are allowed to be driven on pavements in most places.
However check with your local laws as some places may not allow the mobility scooter to be drove on public roadways especially the busier roads.
I've seen several people driving their mobility scooters on the roads and they have not gotten into trouble for it nor stopped and they've passed police who said nothing to them.
As long as you're not drinking and driving the mobility scooter you should be just fine driving the mobility scooter on the pavement.
Also make sure you're watching traffic and other vehicles should move over to get around you as well but you need to be aware of any oncoming traffic.
Ride the mobility scooter down the pavement in the direction where you can see the vehicles coming towards you.