If you want S4S (squared on all four sides) boards, you’ll need a table saw (or maybe a band saw would do)

Bandsaw would be the normal choice, if I'm not mistaken (obviously it has to have enough resaw depth). 150mm is roughly 6", which I think would just barely fit through a 14" Delta or one of its many Asian-made clones. (I've been shopping for a bandsaw lately . . .)

Most table saws would need a pass on each side and possibly some handsaw work to split the remaining middle bit afterwards. Doing the entire operation with a handsaw and/or hatchet is possible but requires more skill and patience than I would have.

If you don’t have a lathe, it’s going to be very difficult, but not impossible, to get it round.

Tool handles don't have to be perfectly round, though. You can just carve the corners off a block until you get something kind of octagonal. I have a couple I made that are rounded rectangles—not perfectly symmetrical, maybe, but comfortable enough to hold.