I'm not sure of the concentration of hydrogen you expect t be evolved or the other gases present but you could consider using a hydrogen leak detector (one that shows concentration rather than just alarms). Example here
Volumetric measurement (water displacement method) of evolved hydrogen gas is the convenient and easily accessible approach.
You can carry out the reaction in a small vacuum flask (a conical flask with a side tube), close the flask tightly with a cork and connect the side tube with the open end of water filled inverted burette erected from a water filled trough. When the photocatalytic reaction occurs in the vessel, the evolved hydrogen gas is collected in the burette by downward displacement of water. The volume of gas gives the rough volume of hydrogen evolved. It should be worked out with aqueous tension value at the room temperature to get the exact volume. The exact volume should be converted to corresponding volume at NTP for general use.
I think the volumetric method is not suitable. If you have a photocatalytic system containing a light source and a photocatalytic solution containing a sacrificial agent, as well as a reactor that fills with argon gas before reacting, the volumetric system may not be suitable. Because if you react without photocatalyst and only with solution, you will have a gas bubble. If even with an empty chamber is reacted (only argon is purged into the chamber) you will still see gas bubbles in the burette and the volume of water will decrease. Therefore, the reduction in water volume can not be attributed to the complete production of hydrogen. Because the gas that is purged into the chamber also starts to expand, begins to expand and enter the burette, and eventually you will have a mixture of hydrogen, argon and possibly oxygen.