I would be more suspicious of a non registered charity. But thats me coming from a finance background and seeing many opportunities to be fleeced.
I don't think thats an entirely fair statement but at the same time I do realise that there are 'those' out there that aren't entirely legit. That said I would think that if you ask plenty of questions, look at the care of the cats and go with your gut feel then you will find the right person to deal with. If you wish to probe into the rescue then there shouldn't be any reason why not so long as your requests are legitimate and reasonable and you do it with the rescue directly not via other sources.
We take calls and visits every day from people going to registered charities and non and have been treated like dirt and made to feel unworthy as a cat owner. I think it has less to do with whether or not you are a registered charity and more to do with principles of that rescue, and the care they give. Some of us smaller rescues do all we can but with limited resources we all have to draw the line somewhere. Also just because they are a registered charity doesn't necessarily mean that money is being spent as it should as it depends entirely on the morals and views of those running it!
As a small currently unregistered rescue I can say that we Spay, Vaccinate, worm and frontline all of our cats before they leave but that does put a massive strain on our limited resources. We are very open adn honest with everyone who walks through our door and treat everyone as an individual. We have no issues with people asking questions looking at our own cats as well as the rescues, standard of care and we also advise people that if they feel the need they can contact our vet for a reference to the standard of care given.
So, personally I would say to you think less about the status of the rescue and more about the care of the animals. If they vaccinate then great but I think you will probably find those with funds will (I hope) whether it be the first or both. Most importantly do they have good hygiene and disease control measures.
Don't go with the first rescue you visit. Visit a few and get a feel for the levels of care and standards that are provided and who you feel most comfortable with.