If it's a male cat & un-neutered you would be able to clearly see his "bits". Can you? Being not neutered doesn't always go hand in hand with spraying etc. they can be separate behavioural issues. What you could do, and I know not everyone will agree with this, is catch the tom cat yourself and take him to be neutered. You can do this either at your own cost, or call the Cats Protection and see if they will fund it. If you tell them there's an entire male causing fights & no doubt adding to the unwanted cat population they will often give you a code to tell the vets & they'll tell you which vets to go to, and will cover the cost. You just have to catch him, take him to the vets & then bring him back. Please don't spray the cat with dye. It's not his fault that he's behaving this way. It's his natural instinct.