Drill it. I just completed my kegerator out of a 1948 General Motors/Fridgidaire retro fridge that looks almost identical to yours except its handle is vertical. Once I took out the shelves, i can fit two kegs and the CO2 tank as well as two cases of beer on the top shelf above the kegs. I think i could probably fit three kegs if i put the CO2 outside. I installed a Perlick faucet and just swap the line between kegs rather than adding a second faucet. I think that helps it looking 'cleaner" from the outside and the chrome blends right in with the style as if it were made that way!
If you do drill, be careful. I have a suspicion mine had asbestos insulation in the door but I can't tell for sure if thats what they used around this time period. Drilling the holes themselves was simple and took all of 15 minutes to complete.
My only real "issue" is that in order to keep mine at 37-38 degrees, my mugs don't get quite as frosty as i'd like in the small icebox. If i turn it up so that the mugs get frosty, the internal temp drops below freezing in the rest of the fridge. Mine is almost too cold, tracking at 37.5 degrees with the knob about a millimeter above "defrost" setting. At mid-range setting, mine turns into a large upright freezer at 12 degrees and I assume at its highest setting, it would be below zero.