Or would use of a sippee cup (the kind toddlers use) be permissible?
Seriously, it’s no more of an issue than it would be having an elderly or ill priest in a church who had problems holding a chalice. The only issue is to make sure to clean up any spills properly. If you had a small amount of Precious Blood in a large chalice, and only consumed by the celebrant, then there shouldn’t be an issue.
Are there any stops longer than about half an hour planned on this journey? If so, save the Mass for then. If not, even a stop of say fifteen minutes might be adequate to complete the Liturgy of the Eucharist and distribution of Communion, and it might be able to be timed for then.