It’s a bigger jump than could be with a mid grade hone.
I go 1K, 3K, 8K.
Essentially you are going 1K to 6 to 8K. It is totally doable, but something in the middle will make the transition faster. I would choose a 3 or 5K hone. For light bevel setting you could use the 3K. It will save time and laps.