As much as I am loathe to give your players any ideas on making their own weapons, I'd allow it to happen on a small scale. Basically, I'd give the player a couple of options and neither is what they're looking for, I'm sure of it.
First one is to make a gun that will glitch on 1s and 2s - double the liklihood of having a problem with it, because it's using cheap materials like those produced with a desktop 3D printer. Additionally, I'd argue that on a glitch the gun breaks. For good. AND it only has a 2 shot capacity (use the stats of the Walter Palm Pistol).
Second option is to get a gunsmith to manufacture a custom gun. There are gunsmiths all over the place that will do this for a price - but they usually retain the rights to produce more of that gun if they so desire. AND these are always based on existing models. So he could take an Ares Predator IV and get some custom work done to it to improve it's cycle rate, suddenly making it capable of burst fire. Or extend the barrel to make it have more range. There's a couple of things that you could do to existing guns to tweak them, but Run & Gun doesn't really cover that material as well as it was covered in Arsenal.
Let's assume you allowed the player to make a brand new weapon, from design to completion. Make the player pass the knowledge skill checks (remember that active skills act as knowledge skills now). Make the player seek out a manufacturer that is willing to do this contract work. Make the manufacturer take the design as part of the payment - note the word "part" as this will not be cheap under any circumstances. Fill the weapon with tracking RFID tags built into the material of the weapon, on the basis that the manufacturer is just covering his own butt for liability. And finally, if you're going to make a custom weapon, make it balanced with the existing weapons. If they're going to make a pistol, make it balanced with the other pistols. This should not be a "better" gun so much as one that fits his/her specific needs. If they want a pistol that does Ruger Super Warhawk damage, with an Ares Predator magazine, and a base Accuracy of 7... no. That's way out of balance. The thing is, most of the variety that one would want is covered by the stats of an existing weapon. If they want to take those stats, and just have it be a "snowflake" gun (that is, one of a kind) then apply the Custom Look bonus from 4th edition. It gives a bonus to social tests involving the weapon, but also makes it very distinctive.
With all this reference to Arsenal, it's probably worth mentioning that Arsenal covers this topic to some extent. Basically they give some basic rules for modifying existing weapons pretty heavily, and treat desktop forges as a bonus to the quality of tools used. Additionally, getting the feedstock is tough - Availability of 10R, and higher for feedstock that isn't riddled with RFID trackers.
So that's the long version. Short version? Don't let it happen unless the player really wants it to happen and is willing to pay the price. Ultimately, it's just not worth it to most people.