Yes, absolutely, a standard Mikuni dual outlet pump will work. I ran my Invader for a couple years with one I bought from DennisKirk, before I rebuilt my original pump. The Kawis had engines mounted so low in the chassis that they used a slightly oddball Mikuni pump that featured a clever anti-syphon device, which acted much like a manual fuel shut off.
If the needle and seats in your carbs are in good shape and sealing, you will be fine. Incorporating a fuel shut off somewhere in the fuel line is a great idea to prevent fuel leaking by the needle and seat when you're trailering the sled, etc.
I usually forget to turn them back on, until the sled starts and dies...
As gixxer6 mentioned, you should be able to find an airbox. Just be aware of a slight difference. The 440 Invader used 36 mm carbs versus the 32 mm carbs on the 340 Invader or the fan cooled Intruder. The rubber rings that fit in the airbox are slightly larger for the 440 Invader....the airbox plastic is the same, but you would have to find the correct rubber ring inserts if you buy an airbox that came from a 340 Invader or an Intruder.