Generally, I would agree with Mike that you can't use a powder safely if you can't find pressure-tested load data for it.
But, you have found load data for the bullet and powder you want to use, except that it uses a .38 Special case instead of a .357 Magnum case. Because the .357 Magnum case is just a little longer than a .38 Special case, AND because the .357 Magnum is loaded to much higher pressure than the .38 Special, it is clear that the powder can be safely used in the .357 Magnum case with a slight adjustment. At least, it can be used for loads that are no more powerful than the .38 Special loads in the data.
The adjustment is to slightly increase the charge weight to compensate for the slight increase in case volume, so that the pressure of the start load will not go too low and stick a bullet in the barrel. (That is a particular concern for 158 grain jacketed bullets in the .38 Special when shot in long barrelled revolvers.)
To do that accurately, you would need to figure-out the difference between the powder space when your bullet is loaded into a Magnum case and a Special case. That is commonly done by weighing cases empty, then filling them with water flush to the mouth and weighing them again to find their "water capacity" in grains. Then you need to do some math to subtract the part of the case volume that will be occupied by the bullet so that you get the volumes of the powder spaces. The load data is then adjusted by the ratio of the powder spaces.
Because you are talking about shooting Special level charges in a Magnum gun, you have a lot of margin between the 18,500 psi upper limit for +P .38 Special loads and the 35,000 psi limit for .357 Magnum loads. So, it is not so critical to get the charge adjustment factor just right. So, I'm going to compute one for you instead of typing-out a lengthy procedure for you to follow with cases fired in your particular gun.
Using the QuickLOAD program to compare the powder spaces in a "default" pair of Special and Magnum cases, I get 15.826 grains of water for the Magnum case and 13.320 grains of water in the Special case when the bullets are seated to the same depth in each case. (The seating depth was chosen to match the 1.434" COL in the Ramshot data.) So, the ratio of powder spaces is 15.826 ÷ 13.320 = 1.188. So, if you increase the charge weights in your .38 Special data by 18.8%, you should get about the same pressure as the Special loads when you load the Magnum cases.
Ramshot's Silhouette data is:
Silhouette 158 HDY HP XTP 5.0 872 5.6 969 16,410 1.434
That is, the "start" load is 5.0 grains giving 872 fps
and "max" load is 5.6 grains giving 969 fps and 16,410 psi.
To get the same pressures in the Magnum cases,:
"start" is 5.0 x 1.188 = 5.9 grains
"max" = 5.6 x 1.188 = 6.6 grains.
Since this max load is still giving only about 16,400 psi in the Magnum cases, I suspect that you might be tempted to load more powder for more performance. That is where I need to agree with Mike. You should not do that without having some pressure tested data that tells you where you need to stop. Some powders can cause pressure spikes when loaded beyond the POWDER'S design pressure in ceratin cartridges, so it is not just a matter of doing calculations to extrapolate the charge weight up to the Magnum pressure limit. Those calculations may or may not reflect reality, and that is why the manufacturers do pressure testing.
If you want to take Silhouette to Magnum pressures, I suggest that you try asking the Ramshot people for some data. Try them at 406-234-0422 or www.ramshot.com