Yes, you can use Uberti parts on Pietta revolvers, though some fitting may be in order. I install Uberti square-back trigger guards on my Pietta 'Navies'; they don't line up perfectly (enough to get the screws in place, but there will appear to be 'overflow', for lack of a better word; this can be filed smooth).
I myself have the same project in mind (albeit on an 1861 Navy), an attempt to copy a pistol made by Millington I saw in a book by Dennis Adler. I've not found a grip assembly on its' own, they do cost around $300 & include the wood grip...from Taylor's & Co, anyway.
I'm considering buying a Sheriff's Model 1873 & changing the grip for a standard Peacemaker grip...I want a Peacemaker anyway & figure it'll save me a few dollars.
The conversion kit I'm using, BTW, is a Kirst kit...a miserable waste of money in my opinion: the pin which fastens the loading gate works it's way loose in very short order as you use it, & will block the rotation of the cylinder as the base of the cartridge hits the loose gate. I'm sure this is fixable, but I've not sorted out how & in the meantime I'm frustrated. For the money spent on a kit, they ought not have that problem.