How do I hit the “Ctrl” key without straining my pinky?

I'd suggest that you don't use your pinky at all - press the outer command keys using the base of your small finger on the relevant hand (the edge of your palm, essentially), this works well for Ctrl and Ctrl+Shift combos.

This method doesn't require moving your hand much and doesn't require any finger gymnastics. I guess it might need a little bit of practice if its new to you, and is completely useless if you have a "flat" laptop keyboard as you need to be able to press in from the edge of the keys.

Since I'm not 100% sure I've explained what I mean very well, here's a quick photo I've just taken of what I mean - my left hand pressing the Ctrl key with the base of my small finger having not moved my hand. For pressing Ctrl+Shift my hand would just be a little further up, to cover both:

Another option is to press Ctrl and the key being modified with different hands if you don't do so already - allowing you to lower the hand pressing Ctrl and avoid the finger gymnastics, but this again will need training and might be slower in general but especially if you happen to have the other hand on the mouse at the time.

Using autohotkey, remap your capslock key as your third control key; the script will go something like this--

; capslock into control key
SetCapsLockState, AlwaysOff
Capslock::
Send {Control Down}
Sleep 500
Send {Control Up}
Return

Since you are supposed to hit the control key on the opposite side of the keyboard of the key that you want to hit, just slide your other hand back to hit it. It may be easier to rotate your hand instead though.

OS X has a built-in way to remap ⇪ to ⌃:

A bit extreme, but you could make a custom keyboard layout where the actions usually provided by modifier key states are accessed with dead keys under the thumbs:

_{On OS X the actions under control or command can't be remapped using this technique, but the actions that output single characters (under shift and option) can.}