It's hard to tell from the pictures how hard it would be to replace the bulb socket with a North American screw-type socket.
As an alternative, I found this website that sells 110v European base bulbs. (There may be more websites because I searched for all of 30 seconds.) Then, all you have to do is to change the plug (or even use a travel adapter) and you're good to go.
If there is a specialty lighting company or electrical supply place near where you live, you could go there with the European bulbs and see if they could match them in 110v versions.