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.
I asked a somewhat similar question a few weeks ago and Poutnik made a smart suggestion that I simply mix the H2 with nitrogen to keep it safely below explosive concentrations, which I set out to do prior to extracting it outside with a fan. So the nitrogen ensure that concentrations are low enough for the fan engine's sparks not to light it on, and the fan extraction avoids both hydrogen and nitrogen accumulation in the building.
You can buy the fans and tubing in stores made for hydroponic gardening. The tubing looks like this:
Also keep in mind that every time you turn an electric switch on or off, a voltage peak occurs which ionises a small amount of air between the contacts and creates a tiny spark, so an electric setup nearby that is turned on / off may be hard to separate from having a "spark", which may be as dangerous as any other sparks if the gaseous mix penetrates the switch area.