Why not flush mount it to the bottom of the desktop? It will be up higher and harder to see, but still readily accessible and able to be forgiving of being pulled in any direction. As stated by someone else above, there are some pretty low profile magnets out there. Velcro might accomplish something similar, but could weaken over time and would worry me more than a couple of strong neodymium magnets.I'd have to use two magnets to make sure the shotgun stays in place, more for stability than anything else. I don't trust the single magnet use and though not as bad as the J hook set up it still hangs lower than I want it to. Especially since it will be under the front third of the desktop so more easily seen than if the hardware was flush mounted to the bottom of the desktop.
If by "front third" you mean the third closest to you, then I'm presuming you don't have a keyboard tray mounted under the desk, unless you're talking about mounting it off to the side of a keyboard tray. If it's a short enough firearm, like a Shockwave or something along those lines, mounted under a deep enough desk or an "L" shaped desk, then you could even mount it with just the butt of the grip toward you and the muzzle pointed away from you if you need to. That gives you less purchase under duress than mounting it sideways, however, but it would be pointed in the general direction of a would-be attacker already when you pull it out and might even facilitate firing it without drawing it if time is of the essence and the assailant is in the muzzle area.