I'm searching for a reasonable timeframe in which a king or courtier of a semi-distant land would be able to receive an extremely urgent message. The world itself is completely different but lets suppose we are trying to make the trip from approximately mainland Denmark to London, England, (but supposing that infrastructure is mostly usable and intact). I will attach a sketch of the actual map, but this comparison is for the sake of scale. (Within the map, our starting location for the messenger is the capital of the southeastern purple kingdom, and the destination is the east coast of the lime green island that is cut off by the bottom margin of the photo). Let's operate under the assumption that we are working with conventional methods of transport available to high medieval civilization (Such as carvels).
Which route would be the fastest realistically? Taking a ship straight from the starting point to the destination, or travelling by road to the port on the southeast of the continent and taking a ship from there. This continent has very powerful easterly currents and winds on the south side, which turn into northerly currents on the east side, and as such vessels sent from the capital would be heavily hampered.
Would there be any other, more efficient method? I'd guess that the only other real method is courier birds, however I imagine that they are not particularly adept at crossing open ocean.
If this is the best method, what range of timeframes would be realistic for the arrival of an extremely urgent message, which is being relayed by multiple different people? (So we can suppose that if our messenger is shipwrecked, someone else will arrive within a similar expected time.)