What is the minimum number of sea crossings or aeroplane flights required to visit all the countries (UN sovereign nations) of the world?

I interpret the question to mean how many boat or airplane trips a traveler needs to make to see all UN sovereign nations, assuming the rest can be seen via land transportation, including use of bridges over water..
From my starting point in North America, I can visit all mainland countries in North and South America.
1 Flight to Australia
1 Flight to Africa for mainland Africa + Europe and Asia (via Egypt)
That leaves only island countries (I count 48 from the link)
Exclude Brunei (on Borneo along with Indonesia)
Exclude East Timor (on Timor with Indonesia(
Exclude Haiti (counted with Dominican Republic)
Exclude Papua New Guinea (shared with Indonesia)
Exclude United Kingdom (Northern Ireland reachable via Ireland)

I count 45 via this sorry attempt.
https://en.wikipedia.org/wiki/List_of_island_countries

That sounds reasonable, Six, although anyone adventurous enough to make it through the Darien Gap from Panama into Colombia, might be one of the few to make the winter overland passage across the Bering Strait! https://www.lonelyplanet.com/thorntree/forums/europe-eastern-europe-the-caucasus/topics/russia-transsiberian-belarus-and-ukraine-sticky?page=2#post_2387594

Yes, but... An air or sea crossing is needed to get from New Guinea to Timor, and another to get to Borneo even though Indonesia is present on all three. https://en.wikipedia.org/wiki/Indonesia Otherwise, you could count North and South America as adjacent to Africa-Europe-Asia merely by visiting France across the border from Suriname or Brazil. https://en.wikipedia.org/wiki/French_Guiana I would also have grave doubts about the possibility of getting to South Korea by land. Geographically, yes, but you try it in practice... https://en.wikipedia.org/wiki/North_Korea

SixShutouts66's calculation sounds reasonable to me. However, as the question referred to UN sovereign nations only, we have to exclude Taiwan. So we end up with 44.