“archipelago” is derived from the Italian “arcipelago” originally meaning “the Aegean sea” deriving in turn from the Greek “arkhi” (chief, as in “archbishop”) and “pelagos” (sea). (Concise Oxford Dictionary). For the Greeks then just the major bit of water around them but the meaning wandered to mean any sea with many islands.
We have “skerry” in English too, a small rocky island (from Old Norse via the Orkney dialect) but it’s perhaps now too narrow to be used as a synonym for “archipelago” which includes more substantial islands (otherwise it would be rather satisfying to refer to the skärgård as the Skerries).
“gård” has also made its way into English as “garth” – COD gives the meaning of “close” or “yard” as archaic but “cloister garth” is used (an open space within cloisters and perhaps a neat translation for “klostergård” without having to go burbling on about small courtyards, though yard too is related to “gård” through Old English “gearth” enclosure).
“Skerry garth” is tempting and there is in fact the odd usage of “skerry garth” in the Shetlands but we’d probably better stick to the Stockholm Archipelago for the time being.