That serial number, according to my Madis/Wilson book, was produced in 1927-28, and is suitable for smokeless powder. I'd say that any Winchester or Remington .32-20 ammunition produced since 1970 should be safe to use.
You may find older/vintage .32-20 high speed ammunition produced for rifle use only that may be unsafe for revolver use...if you find some older ammo, do some research on when it was made and its suitability. Current production .32-20 ammo is suitable for either rifle or handgun...again, do some research.
On this site, Mike Irwin, or Winchester 73 may have opinions on the subject.
Best Regards, Rodfac
Our Flag does not fly because the wind blows against it,
It proudly waves because a soldier's dying breath blows upon it.
USAF Forward Air Controller, 5th Spl Forces,
An Loc, lll Corps, RVN, 69-70, Vietnam Vet '69-'73