Swales aren't all created equal. Swales basically do one thing in a variety of different ways, but it's all about water control.
I would dig out the paths/swales between your beds and backfill with woodchips. It's essentially the moisture battery part of the hugelbeet, but extended to the area around the beds. The constant moisture levels and all that tasty woodchip to eat results in an explosion of soil life, which basically means that much of the soil work is then done for you by worms, fungi, and associate microbiota.
Plus, if you drop that excavated layer of subsoil atop the unfinished
compost and manures you want to be piling atop your woody layer, it gives a buffer zone between where decomposition of the hugelbeet occurs and the root zones of your garden plants, which don't really like those conditions, live.
The paths between your raised beds will act as swales anyways, as long as there's the slightest depression. Do you need to dig them out? No. But you might find it of benefit.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein