I have used standard pistol primers with a number of powders in .357 Magnum without issue over the past 40 years or so. Those powders include Unique, Herco, W-231, Universal, CFE Pistol, Power Pistol, Accurate No. 5, Titegroup and Bullseye. I would not use W-296/H-110 with standard primers, especially in cold weather. Save your W-296 for the future when magnum primers are once again available, or find someone willing to trade some SPM for SP. While your rounds will probably all go bang, using standard pistol primers with the slow burning ball powder will have inconsistent burning and lead to erratic velocities. Also, you will have a lot of unburned powder gumming up your firearm. I am also in the camp of 2400 is dirty, especially with standard primers. I even gave up on Blue Dot because it seemed dirty, even with magnum primers.
I really like W-296/H-110 in my .357 revolvers, but only with magnum primers and a good roll crimp. That will provide the best consistent performance, velocity and accuracy for that cartridge, at least in my experience.