Don,
If your's is really a Remington-made action sent to Sweden to be barreled and stocked into a military rifle, it's a Number 1 (black powder) action, model of 1867. The receiver should measure a nominal 1.312" thickness. A Number 1 1/2 should measure a nominal 1.140" thickness.
As far as I know, Remington never made or sold smokeless actions to the Swedes. By the time the Remington Number 5 (smokeless) action came out in 1897, the Swedes had been building their own actions and rifles for almost 30 years, and had adopted the Mauser rifle. The breech blocks are interchangeable between the Number 1 and 5 actions.
The Number 2 and 4 actions are much smaller and different proportions than the large Number 1 and 5 actions. The Number 3 was the Reminghton-Hepburn, a dropping block target rifle, not a rolling block.
The easiest was to identify a Number 5 action without removing and measuring the barrel shank, is to look for the receiver radial relief cuts on either side of front of the breechblock. A black powder Number 1 action will have them, but the Number 5 will not.
HTH
John