Not usual for a 10-15 minute nap to completely throw out the 'proper' nap. You will find many-a-mum on the way home from playgroup at 11am desperately keeping baby awake for this very reason. A quick shut-eye in car/pushchair on the way home will completely mess with an established post-lunch long nap.
If the stirring awake after 15 mins happens when out and about, try and avoid baby going to sleep in the first place if at all possible. Wait until home and in the cot.
If the stirring awake is after the 'proper' nap has started, it would suggest baby hasn't got into a deep sleep at all. Why not just stay with baby for the first 15-20 mins after going to sleep?
Stand completely still and quiet, interacting very little, but you are there to resettle at first stirring. The idea is to catch baby before actually waking up. If baby wakes up, you've lost. It's very unlikely you'll get her back to sleep that nap.
My DD used to scrunch get face up when first stirring. If I wasn't there to see it, I'd miss it because there is no noise and very little movement (head may turn to side with her face scrunch though). If I caught her at that point then my settling methods (hand on chest, dummy tap, stroke cheek, shush and then stay there motionless) would resettle her in a few minutes. You will have whatever settling techniques work for your DD, the important thing is to deploy them before waking.
Once there's a cry, or eyes open, you've probably missed the opportunity. I'd still try at that point but if she was getting more awake rather than calmer, I'd give up on the nap.
It then depends how knackered baby is, how exhausted and in need of a proper sleep she is. It might be that 20-30 mins awake is enough, then try again. It may warrant an hour. Given the sleep disruption, baby is likely to need extra help to get to sleep when it does happen.