You will have to have a ground (common) connection for the speakers at the switch box, unless your are planning on connecting the grounds of the speakers directly to your receiver. It will work either way, although it is common to have the amplifier speaker output ground(s) appear at the switch box and the speaker ground connection made at the switch box.
To be clear, when I am talking about the ground connection, I am talking about the speaker connection on the receiver that is labeled "-" not the connection labeled chassis ground on the lower right side. The "-" connection on speaker and amplifiers/receivers is commonly called the ground connection or the common connection.
On some amplifiers/receivers the "-" connections as labeled on the 2275 do not share the same connection point internally. They go to different parts of the circuitry and as such damage may occur if they are connected together.
This is why I made my original suggestion. Again, IIRC the "-" speaker connections for the 2275 are common to each other, that is they go to the same place internally in the 2275 and as such using a speaker switch box where these are connected together should be okay.
In the picture below, these are the wires (going to the right) that go to all of the "-" speaker connections on the back of your receiver.
Note how they are connected together and to ground.
So It will not hurt if you connect them together at your switch box instead of running them through a set of switch contacts. Just remember if you replace your 2275 and you want to continue to use the switch box that the replacement unit has all of the "-", common or ground connections (using the different terms for the same thing) connected together internally. This is commonly called a common ground. If not, then there can be damage to the amplifier/receiver.
I realize that I am biased, pedantic, OCD and a number of other things


, but I like to switch all connections, (both the "+" and "-" connections), all though in your situation it is not absolutely necessary.
Remember that is is not a bad idea to have the volume completely at zero when switching speakers and even a better idea to have the receiver/amplifier turned off, all though that is not always done and when switching speakers on a tube type amplifier, there is something to be said for not quickly power cycling an amplifier where the tubes are already warmed up and some like to leave their tube type amplifiers on all the time. And as mentioned before, it is not the best idea to have a tube amplifier turned on with out a load on the output, all though some have done it without issues when using speaker switching devices.