merchant shipping
On thing to keep in mind in this scenario is that this is truly still the age of sail.
any population movements would be slower than during the PL scenario when steam power is available. Sailing vessels are also smaller. The East Indiaman would be the largest transport available and that will vary with the company..
Danes, Swedes, and French all have East India men on the China trade at this time which can be pressed into service to move some people..but probably no more than what...2-300 at a time and that is a stretch.
Swedes will not be able to go to North Germany because of the local devastation and the already short supplies for the German population still there.
Mind you, how many of those states would survive in an organized form is open to question. Some will no doubt fall under the sway of the Danes, assuming they have an organized gov't.
Temperatures will fall rapidly and the first harvest will be bad followed by an even worse one the following year. the largest die off will probably be in those first years before some kind of sustainable equilibrium is reached and depending on how many can actually escape to southern mediterranean ports and encampments. How viable would that be as a temp. measure.
sea voyages, particularly to Asia would be exceedingly long.
North America will appeal to most as it is shortest. France will no doubt send many refugees to the mouth of the Mississippi if they can It would shore up their claims in the newly explored regions there. Spain has vast terr. in the north in Alta California and Tejas and the Rio de la Plata that could also be settled by refugee settlers. Portugal, southern Brazil ( or perhaps Spain's claims to the east bank of the Uruguay could be strengthened ) all of these are closer than distant Australia for instance, which will probably be explored far earlier this time around by the VoC (they have lost a third of their capital in this event in all probabililty, but are still probably the biggest outfit going) or perhaps the Swedes and Danes in a kind of partnership of sorts. Danes and Swedes do have some posts in Africa and the Danes in India that could be used as way stations enroute to the Indian Ocean..but some kind of partnership with the VOC would be necessary and even desirable to give the three of them bargaining strength with the EIC and the larger Catholic European states.
Let the Dutch/German settlers go to the Cape, West Aust. and Tasmania, the Swedes to East Aust. and the Danes to New Zealand. Their remnant Kingdoms would be the sovereigns over the regions in question. In the Short term..Spanish/French and Brits will be involved mostly in the shorter routes to the Americas and protecting and trying to expand their interests there. They won't even be looking at the Indian ocean because of its distance. Obviously the Br. colonies will also be a repository for some Scandinavians and Germans as well. especially if you have a Hanoverian Br. America develop and a Stuart restoration in the Br. Isles. Just were would the bulk of the EIC merchant fleet end up...? or in whose service in that case.
Some kind of bargain will have to be struck with the Hapsburgs as well perhaps that might enable refugees to depart by way of Adriatic ports. And of course there is Venice, Naples and Tuscany as a ports of exit as well