Will mixing hydrogen and oxygen without a spark result in combustion? I plan to do the electrolysis of dilute sulphuric acid. This will produce hydrogen gas and oxygen gas at the anodes. I do not plan to collect these gases, but to simply let it form and release into the air without separating them. Would this carry any risk whatsoever, considering that an electric setup is nearby?
For hydrogen to burn or explode in air, its concentration needs to be at least 4%.

Unless you're using very high power levels, you're unlikely to reach that concentration in the room's air. You could ignite bubbles of hydrogen as soon as they pop at the surface, but if you don't, the hydrogen (with about 1/8 the density of air) will rise quickly, diffusing into the air as it goes.

If you're doing this using a battery, or a small line-operated power supply, there's very little danger of explosion.