Yes, the Laz are Muslims who speak a Kartvelian language (the area has produced a few famous singers lately, like Kâzım Koyuncu), just as the Hemşinli are Muslims who speak a dialect of Armenian.
Just a little note to the Hemshinli; this name is commonly used to refer to the Western Hamshenis, that happen to be Armenian muslims that don't speak an Armenian dialect anymore, yet now speak a Turkish dialect that they call Hemşince.
There are two other groups of Hamsheni Armenians as well; the Northern and Eastern Hamshenis, which are both also known as Hamshetsi.
Both of them are culturally quite similar, and they both speak the same language, which is the Armenian dialect called Homshetsi or Homshetsi lizu by its speakers, although I should add to that that "Hemşince" is the usual Turkish naming for Homshetsi.
The only real difference between the Northern and the Eastern Hamshenis is that the Eastern Hamshenis are Sunni muslims, while the Northern Hamshenis have remained Christians adhering the Armenian Apostolic Church.
I do not have any clear statistics, but I remember that there are about 400,000 Hamshenis worldwide, of which about one half is muslim, the other Christian.