You can get a power roller which you fill with paint and that saves dipping it in the roller tray. They are quite easy to use, especially on ceilings. I found when I used it on the wall, I could have gotten away with just one coat using it. Of course doing the edges, at the ceiling and floor, you'll need to do by hand and try to match the coverage from the roller.
The roller I have is from Wagner. I would recommend it - easy to fill and use, powered by batteries. I will say it was a bit cumbersome to clean it when the job was finished but it did a great job in my opinion.
I didn't find a lot of splatter from the roller once I got comfortable with it and figured out how much or how little paint to release with the trigger.
Look for no or low VOC paint. Latex paints are nearly all in that category now here in Canada, I can't say in the US if that is true. But they are available and that means no paint fumes (most of those nasty fumes were from oil paints).
I'm sure your wife will appreciate your efforts. If she has to do some touch-ups later, I'll bet she won't mind.
Q