is a 5V cellphone power supply stabilised?
Yes. USB is a standard. You can even use 5V power packs for portable gizmos.

Caution: Ken Shirrif have a good post about non-original USB chargers and its perils. (A dozen USB chargers in the lab: Apple is very good, but not quite the best). Read them and learn a lot.

I only use the original charger that comes with the cell or tablet (and that usually last longer that the cell or tablet that it comes with). I don't trust any third party USB charger or car adapter after Ken's analysis