The rosary is a private devotion, so you can pray it any way you like. You see, a private devotion is not part of the liturgy of the Church, like the Mass or the Liturgy of the Hours/Divine Office. The Church’s liturgies are called public prayer because they are prayed within rubrics by the faithful. Private devotions do not have any rubrics that must be followed.

Even so, when anyone prays something like the Liturgy of the Hours alone, they are using it as a private devotion, so they can pray it as it suits them with no restrictions about eating or drinking.
Many people have recorded versions of the rosary which they pray along with while driving. biking, walking, doing housework, and other activities. There are no proscriptions against drinking tea or anything else between decades, or any other restrictions. So, don’t develop scruples about how you pray devotional prayers. They are meant to be aids to faith not burdens to be borne.