The context makes me lean towards “make way for a sailor”: it comes immediately after the statement that the sailor has money to spend and only two days to spend it. This conveys urgency on the sailor’s part and the opportunity for others to get some of his money, both of which would fit with a proclamation that room should be made for him. Also, the “all caps” treatment of “way for a sailor” seems to fit with it being a bold proclamation to make room for him (although, I suppose it would also fit with a proclamation that “that’s the way a sailor does things”.)
To muddy the water further, though, a third possible meaning that occurs to me is that “way” is being used to mean “destination” as an extension of its sense of “path/direction”. So SINGAPORE would be the “way for a sailor”, that is, the place a sailor should go. I’m not familiar with “way” being used to mean “destination”, but, then again, I’m not familiar with it being used to mean either “make way” (without “make”, that is) or “that’s the way [whoever] does things”, either.
But, since “way for a sailor” is juxtaposed against money to spend and two days to spend it, rather than Singapore, this makes me lean towards “make way for the sailor”.
Out of curiosity, is most or all of the movie set in Singapore? Or is it just one of many settings in the movie?