Economical depends on your attachment to the 2 lamps. As for a do it yourself project? If you feel that your skills are up to it than give it a try

I have completely rewired three or four vintage lamps. I know nothing about electricity, but I do have Youtube! The first one was pretty tedious (not difficult) and the others went really fast.

Any problems ship them to me I will rewire them for you!

Way back during WW2 I took a course in Radio Engineering which taught me a healthy respect for electricity. I built a radio, among other things. Of course that was a L-o-o-ng time ago. We used vacuum tubes in the radio. I just wonder how good my memory is. Thanks for the responses.