A 10x4 would only have a drastic effect if you can spin it a lot faster. From a 10x6 to a 10x4, all you are changing is pitch.

I too use the gear analogy (offered by Bottlerocketwar) when explaining props to new pilots, however you might care to note that it is just an analogy. Static thrust for the most part is directly related to prop diameter and RPM. Pitch has basically nothing to do with static thrust. Then why pitch down when moving to larger props? It is to keep the engine running at the proper RPM. If you increase the diameter without decreasing pitch, the load on the engine will increase, possibly to a point where the engine doesn't work well or at all.

So, by moving to a 10x4 from a 10x6, you must rely upon RPM increases from the lower prop load to increase thrust. Engines have a preferred RPM they like to run at when wide open. If the engine is already running at its preferred RPM with the 10X6, you may not see much RPM gain by moving to the 10x4 and you could end up breaking the engine if it over revs.

Pitch loads are pretty much linear, i.e. twice the pitch increases prop load by two. Diameter on the other hand is an exponential function. Twice the diameter is close to 16 times the load. So, in the 10 inch diameter range, a good rule of thumb is you must increase/decrease pitch by 2 for every inch of change in diameter. As you can see, either of the two props Bottlerocketwar listed basically adhere to this rule of thumb. The 11x4 you mentioned would also be a good prop to try.

Also keep in mind that the type of prop can also drastically effect thrust. In that size range (10"), the best props for thrust that are easy to obtain will be APC.