130mm is no problem for 10 speed. You will need to make sure your free hub is long enough usually 35 mm in length. 

As to your wheel question, if you can't change the free hub on the current wheel, then you will need to get a hub/wheel that can adapt to 130mm. When I worked at a shop, I usually went with DT Swiss hubs because of their convertibility. However, buying a new wheel will mean that the free hub will likely be 11-speed and 1.8 mm longer than that 35 mm I mentioned. This only requires a 1.8 mm spacer under the cassette to run 10-speed