no links please
This should help for why Lubavitchers don’t wear streilmels.
As to how a Lubavitcher wears his hat, that is only based on the style and how the Rebbe wore his hat.
Would a Lubavitcher wear a Litvak’s hat?
Yes and no.
If he needs it to daven, a Lubavitcher if there isn’t any normal hat available would wear any second head covering to daven.
If not, why??
Hope that helps
Please ask for any other details