Depends on the social occasion.

At a society ball, go with the former.
Flirting while on a date, go with the latter.

Depends if they can hold a glass or not. Do they have human hands now or paws?

Straws duh.

Depends on how thirsty you are?

I’ve always thought the glasses would have long dispensing necks, like a speculum with just one blade. The glass is inserted into the muzzle, resting on top of the tongue, and the liquid flows into the back of the muzzle to simply enter the throat. Fancy wine glasses have small channels to allow minute amounts of the drink to pass through the dispensing neck to the tongue.