Heisann, Wiking! My daughter and her new husband are in Trondheim.
The .44-40 or .44 Winchester Center Fire (WCF) was developed in 1873. It was first used in the 1873 Winchester lever-action rifle. Because it started out as a black powder cartridge for a rifle with a relatively weak action, it never was intended as a high-pressure round. It was adopted for single action revolvers because it made sense to have a rifle and revolver that fired the same round.
You don't mention your revolver's maker, but I assume it's a good, well-made one. Modern steels are much superior to those of the 19th century. Even so, the best advice I can give is to call the people who made the revolver and ask them if you can fire the rounds safely, then call Winchester and ask them if you can fire their rounds safely in that revolver.
If both makers say it's okay, then have a ball.
Guy N. LaFrance
Collector of Curios & Relics, Maryland Designated Collector
Maryland Shall Issue, GOA, NRA, SAF, JPFO
Grand Army of the Frontier, National Congress of Old West Shootists