Keep in mind, many dowels used for joining have their surfaces altered to allow glue and such. As such, a rougher dowel would, rather than be a problem, be beneficial for such uses.
As to flexing of the bandsaw blade, that is not a problem with even a 1/4" blade, and especially not with a 1" blade.
Try a Net search using the terms "using a bandsaw to make dowels," or variations of that. You'll get many hits. Examples of search hits are below. The first one is the method I used.
https://www.google.com/search?client=firefox-b-1-d&sca_esv=d22a7c5074081a0c&tbm=vid&q=using+a+bandsaw+to+make+dowels&sa=X&ved=2ahUKEwiNzPTFnNqJAxV9OTQIHSGmJXcQ8ccDegQIEBAH&biw=1536&bih=685&dpr=1.25#fpstate=ive&vld=cid:1b0c922c,vid:sNES26a0dWc,st:0
https://www.google.com/search?client=firefox-b-1-d&q=using+a+bandsaw+to+make+dowels#fpstate=ive&vld=cid:ad9dab56,vid:Y3LpxJQKcgc,st:0