I've never played a walnut solid body, but scientifically they are about the same with swamp ash being heavier.
https://www.wood-database.com/black-walnut/
https://www.wood-database.com/white-ash/
They are more alike than alder and swamp ash and I can't discern a difference between the two sonically, though I can tell a difference between mahogany and, alder or swamp ash.
I have walnut furniture in my house and it's no heavier (or less) than oak or cherry, though I find Teak and Mahogany heavier.
The neck will have more of an impact on your sound.
If you like the look, I say go for it.