Vocalists tend to be over-dramatic and hyper-sensitive when it comes to their voices - not much different than reed players complaining about their reeds or brass players complaining about their lips.
Honestly, it depends on how well you warm up, your vocal stamina, and how long you need to sing for. If you don't sing often at all and need to sing for a few hours, then you will probably experience a fair amount of vocal strain. However, if you typically sing for an hour a day, you will have more stamina for the service(s).
For this particular situation, there are three main things I can think to recommend:
1.) Do a nice, easy warmup. Start on a note in the middle of your range and then sing "ah" going halfway down the scale. Repeat this exercise going a half-step down each time. Once you get to the bottom of your range, go the other direction up to a comfortable note without strain.
2.) Arrange the musical selections. If possible, work with the musicians to perform any music in keys comfortable for your voice type. Singing at the extremes of your range is one of the quickest ways to tire your voice. I suppose the pre-requisite to this step would be to know your voice's range, which is a simple process.
3.) Take breaks. Even trained vocalists are taught (or should be taught) not to sing more than 45 minutes continuously without taking a break. If possible, take breaks and rest your voice. If necessary, perhaps even work with another person who may be able to lead a service for you if your voice should fail.
In summation, really, don't worry. It is highly unlikely you'll be doing any damage to your voice - especially since it's only one day. Hydration is good for resonance, flexibility, and efficient tone production. Going without for a day, in conjunction with the suggestions outline above should keep you comfortable throughout the day.