Do you have to dig up shell flower bulbs in the fall in New Hampshire?
Just to be sure we are talking about the same plant, when you say shell flower are you referring to Tigridia pavonia? It’s also called peacock flower and tiger flower, just to make matters confusing!
A publication from the Brooklyn Botanic Garden, titled Summer-Blooming Bulbs (edited by Beth Hanson, 2001), says that Tigridia is hardy in zones 7-10 but in colder areas the corms can overwinter in the ground with heavy mulch or they can be lifted in fall “to ensure their survival.”
This information from University of Minnesota Extension (an area with winters that may be cold like yours) gives suggestions on how to store bulbs:
“Most tender materials should be dug after the foliage dries up or is killed by frost. […] Tigridia pavonia (peacock flower) corm [Storage temperature:] 35 – 40 degrees F. Dig 6 to 8 weeks after bloom or after frost. Cure and store like gladiolus.”
It sounds as if it is safest to dig up the corms and store them, but you could experiment and leave a few in the ground but heap mulch over that spot in the fall.