For the ambitious Princess L to consider: Seeing as how the main purpose is working the glutes/hips/legs, and not the grip, strap used would be suggested. There use to be gripping gloves, some with a hooking device attached, but I do not know if they are still available. Or a person can hold the DB's at a shoulder position, like getting ready to press, while walking. Of course, getting back to basics, place a BB on the back when doing walking lunges. Just my view but step-ups give a much better focus and better stretch, than walking lunges do. Either with DB or BB.
If anyone wants a different slant on the Farmer Walk, than do them using one arm at a time. Alternate this with regular Farmer Walks. Develops better balance, strength and assures both sides are getting equal work. A good core strength movement if anyone happens to be into athletic training. And a stamina builder. Good Luck.