I hate to criticize our Benefactor, but,
"European appliances are 220 volts"
That should be 230V.
It used to be that European voltages were 220V on the continent and 240V on the British Isles. Now the EU has ruled that all voltages have to be 230V +/-. At first, the range (+/-) was wide enough to include both 220V and 240V, but in coming years it will be tightened, and the power companies will have to adjust. This caused a lot of consternation in the British Isle because people knew their "electric kettles" would not heat as fast on 230V as they did on 240V.
" “dual voltage,” which means they work on both American and European current" Should be both American and European voltage.
As for what appliances to take to Europe, my professional opinion is that you should only take to continental Europe appliances with a grounding plug (2 blades and a round pin) or ones with a non-polarized plug (both blades equal width). The non-polarized plug should have a CE mark or a "double-insulated" (square in a square) symbol. You should not take to continental Europe appliances with polarized plugs (one blade wider than the other). Those appliance rely on polarization of the power source for safety (per UL), and continental European receptacles are not polarized.
In reality, you should only take to Europe devices that carry the CE mark. I think all dual voltage power supplies will carry the CE mark.
I'm not familiar with the power source in the British Isles, whether or not it is polarized.