How would you say "my shoe"? Singular.
Like "Where is my shoe?" - I have one, I can't find the other one.
«о́бувь» is more like "footwear". It is already a singular mass noun and does not really have to distinguish between one and many.
If you mean a non-sports shoe, reaching maybe your ankle but no higher, it is usually ту́фля (a dress shoe, or a woman's shoe) or боти́нок (preferred by males to describe their shoes, though, more in spoken speech). High "boots" are сапоги́ (singular «сапо́г»).
And, of course, sneakers and flip-flops are their own thing. If you need an umbrella term, it is still "footwear" (обувь).
But how would you ask about one shoe? ("My shoe" is marked wrong as an answer.)
preferred by males to describe their shoes
Not in Belarus, I guess..? I've only seen «ботинки» written on tags in shops, but never heard anyone use that word, only «туфли». I'm pretty surprised to hear it's 'preferred'.
Depends on the kind of the shoe, the most common one is called ботинок or туфля