As long as it isn't rated "+P+" or the page includes some form of warning against using it in an ordinary .44 Special Revolver, it's safe.
While Underwood and Buffalo Bore specialize in hot loads, they're extremely specific when it comes to advising customers on whether or not their loads are safe to shoot and out of what guns, they need to be, otherwise they could get sued. The only thing that Buffalo Bore does that is misleading is that they sometimes make unofficial use of the "+P" designation by applying it to overpressure variants of cartridges which lack an official +P designation by SAAMI such as their so-called ".380 ACP +P" and ".45 Long Colt +P" loads when neither cartridge has an official +P loading, and what's more, their so-called "+P" loads exceed the 10% pressure increase of official SAAMI Spec +P loads significantly.
So yeah, as long as the .44 Special loads you're looking at aren't labeled as some form of overpressure variant, or otherwise include a warning that they can only be fired from specific guns and are dangerous in anything else, then you're safe.