It appears that you have five canes that are several years old and some one year canes. Ideally you would have canes of all ages with the oldest removed each year and replaced with new ones.
No matter which way you go I think it will be at least a couple of years until you get some fruit. My thought is that leaving the older canes will require the plant to use energy to renew the growth on those canes. Since you don’t want them anyway it might be better to remove them and let the plant direct growth to the new canes.
I’d probably hedge my bet by leaving a couple of the older canes for now and remove them in a year or two. By then the younger canes should start producing for you.