Go through the self-checkout if your store has one. If not, purchase something else along with the Disney GC and use your Target Gift Card to pay. DO NOT ask the Target Cashier anything about it. They will tell you no, but if you don't mention it, then neither will they. Just make the purchase.
FYI - as a result of the huge fiasco and arguments at stores resulting from this recent event, I was told at my store that there is serious talk that Target will no longer carry Disney GCs. I do hope this is merely a rumor amongst employees.