Meclizine doesn't cause drowsiness for a lot of people.
To answer your question, it is safe....and it works better for some people than it does for others. Don't expect to take most antihistamines during the peak of a stimulant experience and then be able to go to sleep, though.
Promethazine, diphenhydramine, doxylamine and the other first generation antihistamines are best for this purpose. Another drug that is very effective is Seroquel (which is technically an antipsychotic but it behaves more like an antihistamine at lower doses - the 25-100mg range).