Can I still motorize Universal Building Set 8034 and other from that time with modern elements?
The length of the wire is another thing to be aware of. The wire attached to the motor in 8293 is only slightly more than 20 centimeters (might be a few centimeters more, I don't remember), you can double that by putting in the switch which has about the same length of wire, but it's still not much. I don't know how long the wire in 8700 was, but it looks longer.

You should also be aware that the new motor doesn't have a pin sticking out that rotates, but a pinhole, if you put in a 2L axle it will look about the same, but the notches on the newer (part 32062 - the older part 3704 didn't have notches) are in a different position (I believe they are in the middle of "each L", while the pictures show that the notch on the axle extending from the old motor is in the middle of the "half L" closest to the motor, the belt wheel was about ½L thick), so you'll have to think about how you place the belt wheel if you want to use a rubber band directly from the axle to transfer the motion. You can work around that with a (half)bush on the axle, but that significantly changes the circumference the rubber band goes around, as thus the gearing. (This section was significantly extended to address Michael Verschaeve comments, thanks goes to him for pointing out the issues I believe I have now addressed)

I don't know set 8034, but from the pictures it looks like it would be hard to fit the new motor due to the increased length.