Putnam Humane society

I believe they take towels and blankets at least.

No, they don't accept any animals beaides cats and dogs, with extremely rare exceptions.

They're a no-kill shelter. They do not euthanize any animals that are under their care (shelter animals). Furthermore, they are not a veterinarian, they are an animal shelter. Their only function is to provide shelter to stray and abandoned cats and dogs, until a time at which someone adopts them. While they do contract with local veterinarians (who may be paid or donate their services) to provide rehabilitation for sick or injured animals in the shelter, as well as to have the animals spayed or neutered and vaccinated, prior to adoption, they do not directly provide any veterinarian services to existing pet owners. The best they may be able to do would be to recommend a local veterinarian, or take in the cat if your decision to have it euthanized was not due to reasons stemming from terminally failing health.

I think 9am to 12PM

I'm sure that they do, as long as they are for medium to long sized dogs.

They are a no-kill shelter. They do not euthanize any animals that are in the shelter. They also do not provide services to existing pet owners, as they are primarily focused with intake and care of new stray and abandoned cats and dog, caring for the shelter animals and finding homes for the animals they have in the shelter. They do not have a permanent veterinarian, nor do they have any type of veterinary clinic. They only veterinary services that are rendered by the shelter, are done so by visiting or volunteering veterinarians, and only to provide rehabilitation to sick or injured cats and dogs that are under their care, and to provide basic immunization, evaluation, and spaying/neutering for cats and dogs prior to adoption. If the decision to have your dog euthanized is NOT due to a chronic and terminal health condition, they would likely accept your dog at the shelter, and try to re-home it. If your pet IS terminally ill, then they may be able to recommend a veterinarian.

There is no such thing as a "cat trap." What you would need is a large, "have-a-heart" trap, which are sold at many hardware stores. These are generally intended to capture raccoons, skunks, opossums and similar animals. They have a spring loaded, or simple weighted gate that is held open by a sear, which in turn is connected to a small tray which can be baited or a pressure platform. When an animal enters the cage and puts weight on the tray or platform, it causes the gate to close behind them, so that it must be pushed open from the outside. However, they generally have no locking mechanism, and rely only on the principle that the trapped animal will be unable to pull the gate open from the inside. Cats are pretty intelligent, and may likely figure out how to open such a trap. Additionally, you are more likely to catch nuisance animals (raccoons, skunks, opossums) fairly quickly, before your cat even has a chance to enter it. You also don't want to have to deal with a trapped skunk.