We’re having the same issue and our current solution is to avoid shipping via UPS and go with USPS directly in the first place. Unless it’s a particularly large parcel, it’s more cost effective to pay a little extra for shipping and avoid the extra labor cost of manually copying down tracking numbers to email to customers. You can’t even copy/paste the tracking number from the shipping label PDF, so the likelihood of mistakes is high as well.
One would think that if enough people do this, UPS will notice a drop in sales and get a solution worked out.