Scooter,
Shotgun powders have been used both shothell loads and handgun loads since the start of smokeless powders. Bullseye was originally a handgun powder and there are decades of shotshell recipes for Bullseye. Titegroup is the powder used in Remington handicap factory loads and it is a very dense powder that leaves a large air gap in handgun loads (it is advertised as being position insensitive). Most fast burning shotgun/handgun powders are position insensitive to all but those interested in chronographing their loads.

In only the past few years have there been "exclusive" handgun powders that seem to me more and more common. Even those powders that are touted as being "shotgun" powders are still perfectly useful in handgun loads. I've gone through a couple of pounds of Alliant 20/28 and find it very good in handgun loads. It burns similar to Unique with about 5% less charge needed. Understandably, Unique is called for in lots of 20 and 28 gauge loads and 20/28 is an ideal powder for these gauges in that it is more dense than Unique so the stack height can be shorter as Unique tended to cause stack height problems.

It's very safe to work up loads with "shotgun" powders in handgun applications if you know what you're doing. It is NOT a good idea to adapt a "handgun" powder (such as BE-86, Sport Pistol or Power Pistol) in a shotgun application.

The OP question is perfectly reasonable being that Unique and Universal Clays are both fully suitable for handgun loads. Hodgdon did make Clays, Universal and International as direct competitors to Alliant Red Dot, Green Dot and Unique respectively and there are plenty of recipes for all six in handgun applications.