Some examples, Pic heavy.
Argentina
Railway Police
Sante Fe and Cordoba Regional Police, 1900 until the 1950's.
Trapper rechambered to 45acp in the 1930's

Australia
W.A State Police , first purchases 1895, phasing out by the 1950's but some mounted units still carrying in 1970.
Victoria State Prison Service, 1890's- 1940's.
NSW State prison service, early 1900's issued to wall guards in 38-40.
Northern Territory Police, 32-20 specifically, 1920's-1940's
1895 year of manufacture W.A Police gun

Brazil Rubber plantation Police- early 1900's to 1930's in 38-40 and 44-40
Canada
Used by the Fishermans navy WW1
Mexico
Purchased and utlized during the mexican revolution by Federal forces, Vallista Cavalry, the Rurales, and some rebel groups, 1910-1920.
Papua New Guinea native police, early 1900's- 1930's. 44-40 , records say gun was favored for being more manouverable in the jungle, less recoil and ammo weight than 303.
UK
Royal Navy- 21,000 issued in WW1 for armed trawlers, merchant ship security, boarding parties and popping( shooting) floating mines.
(This purchase was facilitated by the Canadian government who provided inspectors and intermediaries)

1000 privately purchased for East Yorkshire Regiment when no 303's were available.

I'll add the El Tigre copy in Spain as well, as a million copies were made
Spanish civil war- 1930's, issued to Militias, police, rear echelon guards.
Spanish Civil Guardia- large numbers issued to railways and other civil service regiments from 1923 all the way to the 1970's.

Im guessing a few of the above were using HV ammo(1500-1600fps with 200 jacketed) as it became available after 1903