Kevin,  what little knowledge I have is secondhand but I believe the Winchester 99 is simply the European export version of the Model 96, such that Model 96 parts should fit a Model 99. The risk comes if changes were made to the 96 over its production life, so you would want a parts dealer with knowledge for advice as well as parts. 

I’ve never owned either of those shotguns but have owned a couple of Model 101s. My understanding has been the Model 96 was a reduced cost version of the field grade 101, the differences being mostly but not entirely cosmetic rather than mechanical, e.g. no engraving, sound but straight grained Walnut, an uncapped pistol grip, coarser checkering, metal polished to yield a satin rather than high-gloss finish. 

Frankly, I’ve always thought the ones I’ve seen were classy and understated, particularly those with an “English” style straight grip. The big red “W” on the grip caps of the field grade 101 cheapened its appearance, in my opinion.   

I’d wondered if Winchester hadn’t held Model 96/99 costs down by eliminating automatic selective ejectors, manual barrel selection, screw-in choke tubes, ventilated ribs, and single triggers. Those features, particularly the first one, require significant amounts of skilled labor to fit and adjust to work reliably. (Personally, I like double triggers and non-ejectors, myself.)

However, the 99s I’ve seen at auction in the UK have had ventilated ribs, single triggers and what looks like a barrel selection feature on the tang safety. The uncapped pistol grip is far more elegant than the garish 101 red logo insert.

Put up some photos of your gun and you will likely draw more comment.