Change the Option+R/L shortcuts to Control+R/L

In the first example below Option-L/R arrow does the same after adjusting the keycodes as Control-L/R arrow.

The previous behavior Option-L/R arrow (e.g opening/closing a folder in list view) is lost.

If you want a different behavior you have to modify/precise your answer.

To make this work you have to use a third party tool: Karabiner.

1. Download, install and open Karabiner
2. Open in the menulet Karabiner -> Preferences
3. Open the tab Misc & Uninstall
4. Hit the button Open private.xml
5. Open the file private.xml with an appropriate editor

6. Enter the customized keycode

   <?xml version="1.0"?>
   <root>
     <item>
         <name>Change Option L/R arrow to Control L/R arrow</name>
         <identifier>altlr2ctrllr</identifier>
         <autogen>__KeyToKey__ KeyCode::CURSOR_LEFT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_OPTION, KeyCode::CURSOR_LEFT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_CONTROL</autogen>
         <autogen>__KeyToKey__ KeyCode::CURSOR_RIGHT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_OPTION, KeyCode::CURSOR_RIGHT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_CONTROL</autogen>
     </item>
   </root>
   

7. Save the file

8. Open in the menulet Karabiner -> Preferences the tab Change Key
9. Hit the ReloadXML button
10. Enable the remapping. It should be listed at the beginning.

And if you are really asking for "Option+L/R shortcut on my Mac keyboard to Control+R/L" - which can be read as alt-l to ctrl-r and alt-r to ctrl-l in contrary to the headline - then use

          <autogen>__KeyToKey__ KeyCode::CURSOR_LEFT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_OPTION, KeyCode::CURSOR_RIGHT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_CONTROL</autogen>
          <autogen>__KeyToKey__ KeyCode::CURSOR_RIGHT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_OPTION, KeyCode::CURSOR_LEFT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_CONTROL</autogen>

If you want the opposite (Control-L/R arrow does the same as Option-L/R arrow) use this snippet instead. The previous behavior of Control-L/R arrow is lost.

<?xml version="1.0"?>
<root>
  <item>
    <name>Change Control L/R arrow to Option L/R arrow</name>
    <identifier>ctrllr2altlr</identifier>
    <autogen>__KeyToKey__ KeyCode::CURSOR_LEFT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_CONTROL, KeyCode::CURSOR_LEFT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_OPTION</autogen>
    <autogen>__KeyToKey__ KeyCode::CURSOR_RIGHT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_CONTROL, KeyCode::CURSOR_RIGHT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_OPTION</autogen>
  </item>
</root>

If you want to swap ctrl-L/R-arrow with ctrl-L/R-arrow then use either both of the above keycode changes or this one:

<?xml version="1.0"?>
<root>
  <item>
    <name>Swap Control L/R arrow and Option L/R arrow</name>
    <identifier>swap_ctrllrarrow_altlrarrow</identifier>
    <autogen>__KeyToKey__ KeyCode::CURSOR_LEFT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_OPTION, KeyCode::CURSOR_LEFT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_CONTROL</autogen>
    <autogen>__KeyToKey__ KeyCode::CURSOR_RIGHT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_OPTION, KeyCode::CURSOR_RIGHT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_CONTROL</autogen>
    <autogen>__KeyToKey__ KeyCode::CURSOR_LEFT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_CONTROL, KeyCode::CURSOR_LEFT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_OPTION</autogen>
    <autogen>__KeyToKey__ KeyCode::CURSOR_RIGHT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_CONTROL, KeyCode::CURSOR_RIGHT, MODIFIERFLAG_EITHER_LEFT_OR_RIGHT_OPTION</autogen>
  </item>
</root>

My knowledge of keyboard bindings is that it's difficult to do without installing third party applications. With that said, Karabiner (formerly KeyRemap4MacBook) provides a great way of customizing bindings easily, and should be able to do what you want.