...a vaporetto...and...a ten minute walk...
Some of this has been covered by others so please excuse any redundancy.
With the hotel referring to a ten minute walk, a water taxi may or may not be able to get you much closer than the regular vaporetto stop. Knowing the name and location to the hotel will help determine that.
In a nut shell, there are 3 ways to get from the airport to your hotel. A private water taxi, as you mentioned, is the most expensive by far. I understand there is now a shared water taxi system available but we haven't used it so can't comment. Perhaps other can offer insight.
The next least expensive way is the Alilaguna boat. It takes longer, you do have to "check" you baggage so you don't have control of it the entire time, and you probably will not be able to get a "non stop" line to the area of your hotel. And you may still have a long walk.
The third way is a combination bus and vaporetto (vap.). It takes a bit longer, but that is what we do because we travel with just a carry on each. There are two bus lines that serve the airport. One is ATVO and is NOT affiliated with the vap. system. The other is ACTV and IS affiliated with the vap. system. At the airport you can get a vap. pass for various periods from 24 to 72 (or more?) hours. You can have a one way or two way bus fare added to the vap. pass. There is a good site maintained by the ACTV system that has current prices and such. Can't remember the url so just google it.
If you decide to do option # 3, take the # 5 ACTC bus from the airport to Piazzale Roma. Be sure and validate the vap. pass on the bus. Do not wait until you get on the vap. Also, validate the pass each time you use the vap. Then take to the vap. to the stop closest to your hotel. We've done option # 3 many times. Easy Peasy and cheap to boot.
Knowing the name and location of the hotel will probably enable us to give you specific directions about the vap. line and stops. It may even be possible to use google maps street view to walk the route to the hotel to help avoid getting lost.
Oh, by the way there is a site called veniceforvisitors.com that has a lot of good info. that you might want to check out.