If your EDM guy hates the holes, you aren't going to like it either, especially not trying to do them with a Dremel.

If you are intent on doing this, get a good punch to start your holes:

https://www.amazon.com/Super-Strong-Automatic-Center-Punch/dp/B07RNMD2BK/

Buy a Dremel Fortiflex with a pedal and separate motor to get the load off the part in your hand:

https://www.amazon.com/Dremel-9100-21-Forti-Flex-Stationary-Precision/dp/B00G5R4E9K/

and don't try to rig something with copper wire, the last thing you need is slight eccentricities, they will insta-break your bits. Get some 1/8" shank PCB drills to chuck in your dremel:

https://www.amazon.com/uxcell-Tungsten-Carbide-Jewelry-Engraving/dp/B07ZVSNLX8/

Good luck, I'd drill a few hundred before I touched an actual tool. Order a bunch of bits, expect to break many.