We have a show once a week which involved two fire eaters on stage. They drink the fuel and then spit it out into the air. Obviously, some of the fuel goes onto the floor when they spit it out and has to be wiped up after their performance. The stage has wooden boarding on it and I am concerned about the mixture of fuel, wood and of course fire. I have been assured that this is ok but I am not convinced. Are there any special or additional measures that should be in place for this.   

As a one off they would be right as they use paraffin which has a relatively high flash point and isn't readily ignited as a pool, but if it is a regular thing there will be a potential build up over time of paraffin soaked into the wood, which would increase the overall risk of fire and increase the intensity and rate of spread of fire generally (as oppose to only during the performance).

Most correctly insured fire eaters would have as an insurance clause suitable extinguishers, fire blanket and safety assistant (not necessary dedicated but a member of the troupe not performing at the same time as the others and alternating) on hand and risks should be reasonably low.

Some means of protecting the wood from spills of paraffin to prevent accumulation may be wise.