Shortcut for selecting run configuration in Eclipse IDE

You already gave most of the answer yourself. Start by pressing ALT+R, N and then simply start typing the name of the configuration you want. The cursor should be positioned in the filter field and thus incrementally reduce the list of launch configurations as you type. When you've narrowed it down to 1, complete the selection by ALT+R.

BTW: thanks for the reminder, I, too, was using the mouse way too much in this particular use case. I will stop doing so, now that I gave the answer :)

Since Eclipse 4.12 (June 2019, 4 years later) you can also launch any of the Run or Debug configurations available in your workspace from... the Quick Access menu (Ctrl+3 shortcut)

Note: For performance reasons, the extra Quick Access entries are only visible if the org.eclipse.debug.ui bundle was already activated by some previous action in the workbench such as editing a launch configuration, or expanding the Run As... menus.