My unfortunate experience has been that everything matters to some extent or another. To the OP, what I’m planning on doing is taking advantage of the generous risk-free trial periods offered by some direct sellers like Cullen, Triode Wire Labs, etc. Just choose whichever one provides results or qualities that jibe best with your tastes, needs, and budget based on reviews. The used market, especially for cables, is another relatively low-cost/risk way to go albeit involving a little more work -- but many more choices to be had obviously. Frankly I’d be surprised if you didnt hear a difference with better PCs. Whether it’s for the better or worse is the ultimate question, but my money’s on the former. Definitely worth a shot. The good news is that this is an area that is very cheap (or free) to experiment with in your own system and could potentially yield significant improvements.
Another way way to go that I'm also considering is just to make my own by buying some lengths of good bulk cable and connectors. I'm not handy by any means, but even I'm willing to give this a shot as it sounds relatively simple and maybe more than a little gratifying to do. Some popular makes to explore would be Oyaide, Furutech, Wattgate, Supra, and DH Labs just to name some.
On on another note, have you ever considered modding your Ref 9s? Seems I’ve heard several other owners being really happy with the results. I might consider that even before messing with cables. Anyway, best of luck.