1k is too low of a limit. A 2k or 3k stone will work fine. Also the 5k will give you a sharper edge but it may not hold it. But you can create it.
In comparing results don't forget that the overall geometry of the Japanese knife is significantly thinner. Given some use on the Sab, you might want to thin the edge too and here your coarser stones are essential. Also you may find that a more obtuse angle will work best if the steel doesn't hold an edge well. Oddly these two pieces of advise aren't contradictory. You can thin behind the more obtuse microbevel.
I think you are seeing why I recommend a 2k stone so often