Hesson pointed out 35-year-old Fulton got runs in Bangladesh last October in slow and low bouncing conditions similar to what are expected in the Caribbean, and he brings a deal of experience to the side. Flypaper hands at second slip don't hurt, either.
Fulton's lifeline was a death knell for Wellington's in-form veteran Michael Papps, although Hesson insisted today the door is closed on no one.
The same applies to stocky Wellington seamer Mark Gillespie, the country's leading domestic wicket taker, who has missed out at least partly down to the configuration of the squad. Only three frontline seamers - the settled test trio of Tim Southee, Trent Boult and Neil Wagner - have been picked, with backup from allrounders Jimmy Neesham and Corey Anderson.
Throw in two spinners, leggie Ish Sodhi and newcomer, offspinner Mark Craig, and it's an attack designed to cover all bases.
Hesson is anticipating two spinners will be needed during the test series, with the likelihood of pitches in Jamaica, Trinidad and Guyana designed to favour the West Indian spin aces.
Sunil Narine has proved a handful for New Zealand batsmen more than once in the past, and the now-pardoned Shane Shillingford, his action having been cleared after having to sit out the final test in New Zealand this year, may be equally challenging.
As for Craig, 22 Plunket Shield wickets at 39.7 in the just-completed season, do not roar 'pick me'. He got the gig after expderienced Jeetan Patel, having been chosen for the tour after being absent since touring South Africa at the start of last year, withdrew last night.
Hesson admitted Craig, 27, has been fast-tracked due to Patel's decision but there is a belief he has good allround skills, and gives the ball a decent tweak. Even so, this will be a significant step up.
With Sodhi still a work in progress after getting a working over from the Indians in the home summer, how the spinners perform in the Caribbean will be among the more intriguing aspects of the tour.