Let me start by saying this is not meant to be negative towards you or your idea, just to give you a few things to think about if you decide to put money out to pursue this.
A large portion of my job deals with preventing pathogenic contamination on a daily basis and I use medical grade surface disinfectants constantly so I'm very familiar with this subject.
There are a few points to know about the type of product you would need to make:
It needs to kill the common pathogens found in gyms, including antibiotic resistant staph, and others (not in the gym industry and not sure what else is common there) that could cause people to end up in the hospital or at the very least get sick. If your product doesn't accomplish this you could be included in a large legal mess. Extensive testing would be required to make sure it kills all the pathogens it needs to.
The product would need to be safe for the gym equipment. A lot of EO's are known to damage plastics and other finishes. Any proper disinfecting procedure requires that you leave the surface wet with the product for the 10-30 minute kill time depending on the strength. You may be liable for damaged gym equipment for providing the product.
If you're in the US, the government regulates disinfectants and you would need to go through the process to get your product approved. Due to the serious nature of the diseases that can be present in a gym, it's not something to ignore and hope nothing happens.
The EO's you use would need to be absolutely safe for exposure to every type of person (young, old, pregnant, immune compromised, allergic, etc...). Residue, aroma, and possible mist from spraying will be left behind, albeit in small amounts, but it is something to consider.
And last, that gym is a business with a bottom line. High level medical disinfectants are about $20-$30 a gallon. Industrial disinfectants are a lot cheaper. A properly tested, effective, and approved product with EO's probably could not come anywhere near that cost so you might find you don't have a buyer once you develop your product.
I really don't mean to rain on you, and I'm sorry if it comes off like that; it's not intended to be that way. I just wanted to let you know about some of the risks you would be taking when disease and making sure the public stays safe becomes involved...however...a cleaner with some EO's for cleaning around the house sounds like it could be awesome!