Do you think it would be generally safe to use as-is? The tingle is not a problem per se, and I don't think it would affect the fish, I just don't want to risk a larger shock or a fire. The housing would occasionally get a few drops of water on it, and it's not unthinkable that I would touch it with wet hands.
The tingle is an effect I'm familiar with, and you can get it with 'double insulated' products that have metal casings, such as laptop's charging via their adaptor from the mains, mains powered smart radio's, etc. I have a Mu-So cube radio right here, with a metal top, wearing its manufacturer supplied 2-core mains lead, that does it to me when I stroke the top of the cube!
It appears to be due to capacitative coupling between wiring (or deliberate use of capacitors within the device for EMC purposes). I don't know that it would show up with a dc leakage test, but there is clearly a small ac current flowing.
Some people seem more susceptible to the sensation than others.
I'm saying the effect in itself is not unusual, does not necessarily mean that there is a fault, and doesn't imply it's going to get worse, or spontaneously change to a lethal direct connection to live mains.
You have selected a power supply you judge appropriate, and you have designed and built the load on that, which might possibly, who knows, present a characteristic the PSU manufacturer never envisaged, causing a failure that just might be hazardous.
As it's 'home made' I can't say definitively it's safe. So I think better to provide an earth connection.