Sneaky redirects are typically someone trying to outsmart Google (probably a bad idea). In the Google help documentation it says this about sneaky redirects...
In any situation you should think about your users. In all cases you must send users and search engine spiders like Googlebot to the same place.
Even if you are sending users and search engine spiders to the same place you should still look at why you are redirecting them.
1) Why am I making this redirect?
If you are making a redirect because you are guiding your visitors to the correct information then you are probably fine. If you are redirecting users from your old dog page to your new dog page, then you are not being sneaky. If you are redirecting users from your old dog page to your cat page, then you are being sneaky. The reason you are being sneaky is because someone who is on your dog page is looking for a dog page, not a cat page.
2) Is the user going to like where they are being redirected to?
To build a little on the above dog page to cat page sneaky redirect above, the whole idea of not being sneaky is to provide the user of a webpage what they are expecting. If you went to a store that called itself "Ice cream place" and that had signs that said "Ice Cream Sold here" then you probably expect to be able to buy ice cream there. It would be a disappointment if you went in that store and you find that they did not sell ice cream, they only sell clocks. In the same manner, it is a disappointment for a user to visit a page that says it is about "dogs" and end up on a "cat" page.
If you keep users in mind, it is easy to steer clear of having any "sneaky" redirects. Provide for your users a pleasant experience. The less manipulated your users feel while using your website, the more likely they are to appreciate your site and return to it.