Check out Ceasar Guerini site. They have several utube tutorials and one of them is a couple of minutes on stock care. I believe your Rizzini has oil finish, which is similar/same as Guerini.

 

Just read their manual about their O/U, they say there, "After the stock on the shotgun is cleaned it can be rubbed with boiled linseed oil"
Got some Scherell's Schaftol Premium Gold oil in the cabinet, that I used on my Carl Gustaf rifle. Would that work for the Rizzini also?

 

Oil finishes don’t like sunscreen.

 

I use nothing but Howard Feed n Wax. Available at most big box hardware stores. A bottle lasts a long time. Feed-N-Wax Wood Polish & Conditioner | Howard Products

 

That would come in handy if I'll head out a rainy day coming

 

Wood doesn't get refreshed until it shows significant wear. Then it's time to strip and refinish with about 12-15 coats of Tru Oil. Tru Oil is very forgiving to use.

 

I like Renaissance Wax for my oil finishes.