It shouldn't make the slightest bit of difference to your third party video editing software which edition of Mixcraft you use.
However you wont be using Mixcraft 64 bit version on a 32 bit windows.
With all that said , theres no sensible reason to be using a 32 bit windows in 2018. The fact your limited to 4gb max makes it a bit of a non starter. I dont think they even make PCs anymore with that low ram. If 4GB is all you have however I'd include upgrading to 16 or 32 gig ram as well, then upgrade to windows 10. You won't be able to get a 64 bit windows 7 anymore, its not sold , its not updated, and except with special support agreements larger corporations sometimes make with microsoft its not supported. its historical software. And since windows 8 is a dumpster fire. Just skip on to windows 10.
Windows 10. Intel i7 quadcore something. 16gigs ram. assorted mech and SSD hard drives.
Focusrite liquid pre 56. 2x Golden age 73 pres. FMR Audio RNC compressor.
Tascam 38 tape, and Yamaha 8 track cassette portastudio like a boss.