There are certain defences that are known (canonically) to work against dementors. We can dismiss the most obvious;
The Patronus charm is certainly the method with which Harry is most familiar. This isn't especially surprising since his teacher was arguably the "go-to guy" when it came to teaching the patronus charm and massively in favour of them over other methods.
Ghosts can block them (as evidenced in HP and the Deathly Hallows)
And he set off. The Dementors’ chill did not overcome him; he passed
through it with his companions, and they acted like Patronuses to him,
and together they marched through the old trees that grew closely
together, their branches tangled, their roots gnarled and twisted
- They can't see someone Animagus form (as evidenced by Sirius' escape from Azkaban) as their mental state is too alien. Obviously the number of Wizard animagi who could use this technique is vanishingly small.
So what method could Snape favour? Well, we know of at least one other way of dealing with a dementors. By controlling your emotions and thoughts you effectively become invisible to them:
Dementors can’t see, you know …’ He swallowed. ‘They feel their way
towards people by sensing their emotions - HP and the Prisoner of Azkaban
‘It was as if someone had lit a fire in my head, and the Dementors
couldn’t destroy it … it wasn’t a happy feeling … it was an obsession
… but it gave me strength, it cleared my mind HP and the Prisoner of Azkaban
It strikes me that that Snape, a known specialist in Occlumency would prefer a method based on concealment over the undeniably showy (but dramatically more confrontational) Patronus favoured by Lupin.
This also fits in nicely with the traits that JKR assigned to each of the houses. Snape (a Slytherin) would definitely seek to use a method based on resourcefulness and cunning whereas Lupin (a Gryffindor) would plump for a technique that focused on courage and daring.