Windows RDP client that allows key mapping and easy use of Function Keys
The easiest way might be to disable the Fn key. Since you say that using Fn+F10 works, you could go into System Preferences > Keyboard > Keyboard, and enable Use all F1, F2, etc. keys as standard function keys. This way you no longer need to press Fn to send F10.

The second solution is on the PC side. You could install a utility such as AutoHotkey on your PC and remap the keys there. That way the keybindings will only work on the PC. Lifehacker has nice looking tutorial about this. In AutoHotkey, you can decide which applications the shortcut applies to, but in your case it seems like a global hotkey would work since it is running on the PC side.

Another solution might be to try one of the ways to create keyboard shortcuts menitoned in this Lifehacker article. This article's goal is to help you do similar things that AutoHotkey let's you do on the Mac.