You'll get in here via the smaller island, which is a military area. It means that in the island of Pikku-Musta you're not allowed to turn off from the road. That's all, no special permissions required to walk through.
Should you need to know, the ferries to Suomenlinna depart from the Kauppatori market square (cf. the user's web page for coordinates). The cache shouldn't be too hard to find.