Hi, D!
Great question!
We've stayed in several 1 and 2 bedroom villas at
Bay Lake Tower at Disney's Contemporary Resort and, to be honest, I wouldn't rely on a photo or memory of one particular villa when determining if you should bring a filter which hooks up to a faucet. Finishes and features sometimes change from time to time, so I'd hate for you to have brought something which could have been used in one villa, but is no longer compatible.
Instead, have you considered bringing a filtered pitcher? Placed into a suitcase, it would barely take up any extra room, since it is hollow and smaller items can be neatly tucked into it as well. We often ship a box of supplies to our own attention at our Walt Disney World Resort hotel, including such things as an extra pitcher, aluminum foil, and shelf-stable edibles we can prepare for light meals. This, too, would ensure that you'd have the filtered water you crave, without having to worry about that kitchen faucet. (You can also check a box of such supplies if you're flying down, but this may incur an added baggage fee, depending on your airline.)
Address your package as follows:
Bay Lake Tower at Disney's Contemporary Resort
4600 North World Drive
Lake Buena Vista, Florida 32830-8413
ATTN: (include your name, dates of stay and that you are a guest)
All other resorts' addresses are available on their homepages on WDW's website, making shipping packages to your resort simple. Fees and location of pickup vary based on location; as BLT is at Disney's Contemporary, which has a Convention Center, that package will be held for you at the Business Center for a nominal fee.
Have fun planning your stay at the beautiful Bay Lake Tower, D! Send more questions as you think of them; we love to help!