Well, what are you defining as stress? The fact that it doesn't like being moved? Appetite changes? histologic changes in the liver? Difficulty swimming? If you're concerned about moving the fish, the least 'stressful' way would be to introduce it directly into the DT, but I hope you're not advocating that.
The known ways of treating ich are: Tank Transfer Method (TTM), Hyposalinity, Copper and Chloroquine Phosphate.
I've used hypo - and aside from the fact that there are known isolates of crypto that are tolerant & can survive hypo, it's difficult to maintain the proper salinity. You are essentially right on the border of what the fish can tolerate. I clearly remember coming down one morning to see a fish almost dead because the salinity was too low. I find it hard to argue that that isn't stressful on the fish.
Now for copper - like all drugs, it is also toxic to fish, it's just much more toxic to the parasites and most fish tolerate a therapeutic level fairly well, but higher levels of copper are known cause liver issues and fish routinely show appetite changes and stop eating. I've also had a fish die from raising the level too quickly. Again, it's pretty clear to me that copper can be stressful on fish, too.
I have never used Chloroquine Phosphate and it's relatively new, so much less is known about it's effects on fish. It is expensive and difficult to get and there is anecdotal evidence that some species (i.e. hippo tangs) don't tolerate it. I'll count death as stressful.
Tank Transfer Method, if done properly involves putting the fish in a tank, waiting 2-3 days, then transferring it to a separate tank, then repeating this again in 2-3 days. You repeat this process 3 times, so it involves 3 extra transfers of the fish. Ideally, you have the temperature and salinity of the successive tanks matched, so there is no shock from the new water. No fish enjoys being caught, but if done right, there is no injury to the fish and they rapidly adjust to their new home. If you are using two 10 gallon tanks, I challenge you to convince me that the fish knows the difference between them.
Buying, moving and quarantining a fish is stressful on it, no matter how you slice it, but I find it hard to argue that tank transfer method is more stressful than any of the other methods we employ. Indeed, if you truly do consider it barbaric, then you should consider our entire hobby barbaric and quit keeping fish altogether.
Edit- I personally use copper, primarily because it treats other things besides ich, but if I were only treating ich I would have no issues with TTM