I don't know for sure if an Uberti will fit or not, Pietta is different I think.
I own two Belgian Colts, but I have not tried to put a Conversion Cyliner in them. Uberti parts will sometimes swap into otiginals, and the Belgians were built off the originals so........
Can I ask what your S/N is? to date I have the newest one that has come to light, both here and in Europe. S/N 18408 made in 1972, my other one was made in 1961 S/N 2999
Please to to CAS City and go to the Forums, then click on STORM and search for Belgian Colt and you will find Long Johns Wolf(Bootsie was his old alias) and email him and he;ll send you a questionnaire about your pistol. we are trying to garner all the info that we can about these great guns.
That's not the one with a stock is it?