Perhaps, although I'm a native, American-English speaker, my language studies have made me too flexible in some ways. I think both of these are meaningful. The second, "Can I have a minute of your time?" is much clearer and preferred. The former, however, is intelligible and sensible. I'd probably hyphenate it thus: "Do you have time — for a minute?" The grammar doesn't quite mesh, making it sound as if the last clause is separate, an afterthought, but still perfectly sensible in context.
If you do study language, then you understand better than most why English rules do not apply to other languages, and vice versa.
"Do you have time - for a minute?" does not sound effortless, natural and standard, as "Can I have a minute of your time" does. "For" is not included, neither in the Swedish nor in the English refrains.
Time for a cocktail? Time for a smoke? iIme for a break? All yes.
Time for a minute? Nope.
Sorry about the late answer. You can skip tid but it's more idiomatic to keep it. We also often use this kind of sentence without specifying the amount of time, just saying Har du tid?
You could also say Har du en minut över? – closest translation might be 'Do you have a minute to spare?'