That's not an easy trip.
There are currently no ferries between the UK and Denmark, Norway or Sweden. That means you have to go through France, Belgium or the the Netherlands. If you want to maximize time on a boat, Newcastle->Amsterdam is probably your best choice. Boats are slow: that ferry takes about 16 hours and covers just a small fraction of the total distance. On the upside: it has restaurants, cabins, etc.
You will also have to get onto the Danish Main Island. With a car you will most likely have to take the ferry from Puttgarden to Rødby. Trains tend to go up north through Jutland and take the Great Belt Bridge. That's also an option for a car, but it's a big detour. Between Denmark and Sweden both cars and trains can take the Øresund bridge.
(more ferries from the comments and other answer).
Instead of Puttgarden/Rødby you can take Rostock to Trelleborg and bypass Denmark all together. Technically, you can also do Sassnitz to Ystad but that's too much of a detour.
You can also use Google Maps for a direct driving direction. It's a LOT of driving and of course, non-UK Europe drives on the right side. The quickest route seem to go through the Channel Tunnel and than takes the Puttgarden/Rødby ferry (32 hours). You can avoid the car ferry by driving over the Great Belt Bridge (33 hours).
It's a rather convoluted trip. One option is to go from Skye to Inverness, Inverness to Paris and then Paris to Stockholm. Going through Paris is quite the detour, but it actually looks faster than getting off in Calais and taking the train from there.
You can certainly combine trains and ferries. You can take the train to Newcastle, ferry to Amsterdam and then train again to Stockholm.
This is a difficult trip that will require some planning. It will take multiple days and you probably want to put some overnight stop(s) in there to rest up. A lot of this depends on the nature of the medical condition and what your parents are comfortable doing (or not) in terms of driving (left and right), schlepping luggage, maneuvering train stations in different countries, long ferry rides on rough seas, etc.
Ferry Source: https://ferrygogo.com/ferry-to-denmark-from-uk/#:~:text=Unfortunately%2C%20there%20are%20currently%20no,to%20Denmark%20via%20The%20Netherlands.