Upvote:2
You appear to be qualified to apply for an e-Tourist Visa (eTV) which if granted should allow you to enter India after having visited Nepal and catch your return flight from Delhi. This takes a minimum of four days but is all online so where you are does not matter. An eTV is valid for a single entry (except to certain areas which you should not need to visit) over a 30 day period so you could apply before reaching Nepal.
This facility is in addition to the existing Visa services.
So, I think, should not interfere with your existing visa.