Why not just use a 11-32 or 11-34 8 speed cassettes? Are the jumps in a standard cassette like that not workable for you? You'd need a Shimano 8 or 9 speed rear MTB rear derailleur, but they are readily available new and used and whatever price point you want. They work with 8, 9 or 10 speed cassettes and road sifters - I've done it several times. (I might have missed it - road or MTB shifters?) I usually buy mine on EBay, used Deore, XT, etc. I think there's new ones too. You just need to make sure the RD will go as large as 34 or whatever you're shooting for. Sometimes you can fudget a couple of teeth on that. I don't think 10 speed MTB RDs will work with road shifters.
But, regarding mixing sprockets from two cassettes and shifting quality, if you really think you need to do that, it will most likely be just fine if the jumps between gears isn't crazy.
Mine isn't a Shimano example, but Campagnolo 8 speed indexed. I mixed from two Miche cassettes. The rear shifting is fine. Frankly, I think it's perfect-or close to it. If "perfect" is A+, this shifting is A- at worst. My guess is that it would be similar with a Shimano mix and match cassette.
You will be limited to the lock ring that is matched to the smallest sprocket on one of your donor cassettes. If I were you, I'd try whatever combination will get you a small sprocket you can live with and not make a crazy big jump to the second sprocket. Maybe look for a "junior" 8 speed cassette as one of the donors because they come with 13t or 14t would have an appropriate lock ring.
In my case I was only trying to get a 11 or 12-28 which wasn't available. What was available to me, time, place and cost, was 13-28 and 12-21. So I used the 12t small sprocket and 12's lock ring. Then I just chose the sprockets from whatever cassette that gave me the jumps that were reasonable (not difficult for a 12-28.... your case will be different). Getting up to 34 and not needing the high gears, it makes sense to get that small sprocket and lock ring as big as you can.
But based on my experience, yeah, the shifting might be sub-optimal with non aligned sprockets, I doubt it. Even so, my guess is that it would be satisfactory to you, definitely worth a try.
Last edited by Camilo; 11-22-22 at 11:41 PM.