I'd go with carbon dioxide $\ce{CO2}$ as a rather convenient gas which is non-flammable and doesn't require special equipment or exothermic reaction to synthesize. Common ways of obtaining $\ce{CO2}$ gas are:
- Dry ice + ambient temperature above $\pu{−78.5 ^\circ C}$;
- Carbonate + acid. These reactions rarely have significant thermal effect. One of the best mixture would be sodium bicarbonate + citric acid + water. Assuming dissolving of citric acid is endothermic and takes some time, prepare the solution of citric acid beforehand.
$\ce{O2}$ and $\ce{H2}$ are rather dangerous in terms of flammability, also common synthetic methods require exothermic reactions.
$\ce{N2}$ is inert, but not easy to come by; the most effective way of obtaining nitrogen would be thermal decomposition of azides $\ce{M^IN3}$ and ammonium nitrite $\ce{NH4NO2}$.