Personally, I don't think the cab is all that sexy. But the controls are rather unique and interesting and I am a big Atari fan.
There's a strong erm... opinion that maming unique arcade cabs is a sin. Salvage and restoration is usually the preferred option. Failing that, trades seems to be on order. In fact, look into trading the cab for another generic cab in better condition. My opinion would be to trade/sell it for a better fitting cab since your woodworking skills aren't up to snuff.
But try to be realistic. One topic that's almost never discussed is finding replacement monitors for a reasonable price. That's probably why your Paperboy is missing its monitor, it was taken to replace the monitor on a different game. That's the same reason why the monitor in my Hang-On cab was literally cut out. Some cabinets (not yours) require monitors that are damn near impossible to replace. So finding certain sightless cabs (regulars will know exactly which cab I'm talking about here) leaves you no other real option but to sell the parts (I see those near useless PCB's on eBay all the time) and MAME the cabinet.
<grabs fire extinguisher>
So ask yourself these questions.
How badly do you want a MAME cabinet as opposed to a Paperboy cabinet? Do you actually like Paperboy enough to tide you over until you find that "perfect" cabinet?
How easy and/or costly is it to replace the monitor? Keep in mind whether you choose to use a true Arcade monitor, TV, or PC monitor and your sources for each.
If you choose to restore, How much work and money would be required to do so? Can you recover those costs if you sell the cab in the future? Same if you choose to MAME the cab.
Is it possible to offload the cab in its current condition in exchange for a cab better suited to your needs? That translates to possibly less work modifying the cab and lower costs for parts.
Take me for instance. I prefer real hardware over emulated any day. As much as I would like to restore my Hang-On cab, realistically, sourcing correctly sized Arcade monitors locally has proven difficult. That would force me to have a monitor shipped in from outside the area driving my costs up. Since I already have several +19" monitors sitting around, the path I've chosen is a reversable MAME cabinet. Though I know deep down in my heart, once MAMEd, no cab ever goes back. IF I can find an arcade monitor suitable for the cab before I construct the CP, then I'll re-evaluate my decision accordingly.