You can swap the axles/spindles out, provided the old and new ones are the same diameter. The problem is, you'll likely need a cone spanner/cone wrench (not sure where you are, so I'll use both US and UK terms) to do that. The new wheels should fit your bike though, the spindles are shorter on quick-release wheels than on nutted ones. What do you mean by saying you have a tensioner on the other side?