Hi Saundra,
I doubt you'll have any trouble on Regent Seven Seas. There ships are smaller than the mega ships of today, but they are as bigger than the ocean liners of yester years. Most Alaskan cruise ship stay in the calm waters of the inside passage, where most days are like sailing on glass seas. You probably wouldn't have any troubles with stability on the Regent Ships.
The Cruise Junkie web site lists all the events at sea.
They do list Regent for a few minor things like propulsion problems or cancelled cruises, but really if you look at their record and compare it to others they have very few incidents.
Right here on Cruise talk we list the CDC Inspections scores. Though not safety per say, it would give you an idea of the line's attention to detail as they list the latest health inspection scores.
I hope you have a great cruise. We have occasionally considered Regent, but they end up just a bit out of our price range. Everything I've heard about them is that they offer a fantastic cruise experience.