Best Hidden Power type for suicune?

I would keep electric because its a nice offensive type.

You can't change hidden power! Try to ;-)

Electric doesn't have a good synergy with Water (vs Ground and Water).
IMO the good ones are Fight, Ground, Rock and Water of course. Rock is particularly interesting (x2 to Ho-Oh/Charizard/Moltres)

Best hidden powers are them with 4x dmg against oppenents.
Fight ( tyranitar)
Rock ( all fire and flight mons)
water/gras ( golem rhydon), but water has the advantage of stab

Suicune has little to no offensive use.

The only use it would have would be if Niantic allowed certain legendaries for Gym Defense. I think this would be great, as certain legendaries, like Suicune, or the Regi trio in Gen 3, are defensive in nature. And even within the Pokemon games and the competitive scene, some legendaries were more "legendary" than others, so to speak.

Because of Mewtwo's mammoth base stat total, maybe he could still be banned, but I don't see any reason why we can't have Suicune defend gyms. With its defense, it could put in some serious work.

Assuming Suicune could one day defend gyms, hidden power ground or hidden power fire could help cover its weaknesses.

So let's look at it:

Extrasensory: 12 Damage 1.1 Cooldown 10.91 DPS 10.91 EPS
Hidden Power: 15 Damage 1.5 Cooldown 10 DPS
10 EPS

So in General, ES > HP as a neutral option.

If however, HP gains SE against target then IMO doing 3.09 extra DPS is worth .91 less EPS. However, it's slower and less dodge worthy.

There are too many what ifs here to mention but really the only way it shines is with double super effective.

HP Fighting + Hydropump wouldn't be as good as Machamp or Poliwrath vs Tyrantir but would probably be competitive with Vaperon for 3rd place.

HP Rock + Hydropump wouldn't be as good as Golems for Ho-Oh or Moltress, but might come in 2nd or 3rd.

HW Water + Hydropump isn't as good as Vaperon for Golem but it might compete close to Venusaur for 2nd

All in all, there is NOTHING it will ever be first at. But there are a few niches where if you don't have 6 of the ideal that it could come in 2nd or 3rd.

As a side, if I were Niantic, I would make Hidden Power more special. If they kept the damage and decreased the time to 1 second (DPS 15 then), or bumped the EPS to 15 or 20, then Suicine might have some fun offensive uses.