Assuming that your flight would land at 3am, you should be out by 3:40 (take 15-30 min for immigration, another 20 min for baggage reclaim) or 4:00 max (3am is the end of the wave of arrivals from 9pm-2am roughly, so terminal congestion is reduced).
If you are a single woman, kindly arrange airport pickup through the hotel.
If not, chill and just take the radio taxis. There have been not one instance of any trouble with them. Make sure before the driver starts off, he calls your hotel (give him some 5-10 rs extra for the talktime if u so wish), and gives his car number, and his mobile number to them and ideally gets a callback. That ensures safety. You are ALWAYS safe with AIRPORT RADIO TAXIS (Easy Cabs in Delhi/Hyd/BLR, Meru in Hyd/BLR)
For the really paranoid ones, Pepper spray is legal - very commonly sold in delhi chemist (pharmacies) shops. for 400 bucks www.knockoutspray.com.
Delhi cabbies (the black/yellow ones) have been in cases in the past. Sticking to common sense will ensure safety:
a. Take their mobile numbers on sitting in the car.
b. Make sure they enter your destination address clearly with the police constables on duty (A MUST)
c. Make sure you have a working cellphone (112 works for police control room even for intl roaming phones).
d. Lastly, get him to speak to hotel staff, give his phone number and bestest arrange a callback to verify. That will eliminate any instance of negative behavior!
the cabs are there all day/night. The night arrival peak is around 10pm to midnight - so you are arriving amidst LOTS of people - there are lots of people departing (midnight to 3am is fav time for europe departures) - taxis is least of your concern - you'll have enough hustle bustle on your drive.
If you can still get the next dest (jammu/srinagar) hotel owner to speak to the driver (as I posted the link above) - he'll know that he can't take you for a ride - else if it had been earlier, get him to speak to any IMer.
Radio taxis are perfectly safe and that time there's enough (not lots but enough) on the road. They charge 30 US Cents/km.
Of course, if you feel still unsafe, you can hire a Hertz cab (about 30-50% costlier IIRC in my company - don't know airport rates) - that is safe as safe can get, but it burns a small hole in the pocket :)
FYI: ALL taxis at the airport are prepaid (dont recall, some union/police rules) - which means that you NEED to look out for "EASYCABS" or something which says Radio taxi. Look below for more. Hertz ofc, looks the same globally!
Take care and welcome to Delhi!