Ah... OK. I think I understand better now. So you have a tiny, 'toy breed' puppy--I was assuming something more average sized, like a Labrador Retriever. Yep, that petite puppy should fit into a typical hand sink easily (doesn't require a dog grooming tub).
Also, when you used the words 'bad infection', we all naturally assumed the condition was one that could indeed 'infect' other dogs. Something like a fungal or bacterial infection. I think perhaps what you really meant to say is that the pup has some sort of 'non-infectious skin condition'? Totally different situation, if that is the case.
Just as a 'heads up'... be sure to check online the requirements for transporting your pup across state lines for all of the states you will be passing through enroute to FL. You will likely need to carry specific veterinary paperwork, such as vacc records & a current veterinary health assesment, with you as you travel. If you are flying, then the airlines will have specific paperwork requirements also. Proof of current rabies vaccination is the biggie, of course--make certain you not only have a rab vacc collar tag on the dog at all times, but also the actual signed paperwork with you to back that up.
I would assume that the WDW kennels have also already let you know what paperwork they will require, what vaccs the puppy must have prior to boarding with them, etc.. I'm guessing you have likely had these taken care of (the bordetella/bronchitis series, for example), since you had originally planned to board the pup back home... But the disease risks in FL may be somewhat different than what is common to New England. So you may want to double check what the potential exposure risks are, and which vaccs are considered most appropriate for your destination, prior to traveling. With a puppy (particularly one who is currently dealing with some ongoing health issues, and may already be stressed), you just need to be careful & do what you can to minimize the potential risk of infection.
Best wishes for a wonderful WDW vacation!