You're right it is an odd scale. Whats worse is that the kit is actually a mix of scales. The hull is 300-ish and the superstructure is 350-ish.
There are no deicated replacement details for it in the 300 scale range. There are plenty of USN details available in 1:350 scale, but nothing for a Perry per se. In 1:350 scale, Gold Medal Models makes some hull numbers and deck lines. Iron shipwright makes deck lines, flags, and division/squadron marks.
The specification for modern US Navy Haze Gray is 27260 - Testors MM Neutral Gray is 37260. a good match. I prefer to add a drop or two of white to the mix. For decks - MM Gunship Gray and Engine Gray for new flight deck. My favorite antifouling red is American Tradition Red Primer from Lowes. White Ensign Models Colourcoats line of paints is an excellent out of the bottle match for each of these colors
Using 1:350 details on a 1:300 scale kit will look about 12.5% small [(350-300)/300]. As a matter of personal choice I try to not mix scale differences more than 10%. However, the choice is yours.
The better large scale kits of the Perry-class frigate are 1:350 scale resin & brass. Yankee Modelworks makes a long-hull Perry sold as the Reuben James. Irin Shipwright makes a short-hulled Perry sold as the Clifton Sprague. The 1:700 scale Perry by PitRoad is also very nice