Yes, you can choose to take a different reaction
When you ready an action, you can later use your reaction to "release" the action you had held in response to a certain trigger. From the "Ready" section, PHB, p. 193:
When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger.
This proves that you don't have to use your reaction, you can choose to do so or to ignore the trigger. But you're still holding your action, so if you still have your reaction, you can potentially react to a later trigger.
However, there's nothing written that precludes you from taking another reaction, say to cast shield or feather fall or make an opportunity attack or "something else"1, just because you happen to be holding an action. Of course, if you did use your reaction to do "something else", this means you have wasted your action, since you would have now used up your one reaction to do "something else"; in fact, the same section (same paragraph even) reminds you of this:
Remember that you can take only one reaction per round.
Although this was likely in the context of preventing the same held action being released multiple times, it also implies that if you use your reaction to do "something else", you can no longer release your held action. Furthermore, note that if this held action was a spell that required a spell slot, then this spell slot will be wasted (see PHB, p. 193); it cannot be "re-purposed" to cast feather fall or shield or anything...
1 To be clear, the "something else" you can do with your reaction that I refer to repeatedly above is only referring to something that you could have reacted to even had you not readied your action, such as casting shield (which has it's specific in-built trigger), making an opportunity attack (which has it's own trigger of "something that moves outside of your threat range") or any class feature that uses a reaction in accordance to a specific trigger (such as a Scout Rogue's ability to move away from enemies if they end their turn within 5 feet of them).
In other words, something that already had it's own pre-existing trigger. The only thing you can do with your readied action specifically is do that one thing that you prepared for, triggered by your specified trigger. However, this does not preclude you from reacting to these other pre-existing triggers (shield, feather fall, opportunity attacks, etc), but at that point you are no longer using your readied action; that is effectively being "thrown away" in favour of using your reaction in a different way (a way that you could have done anyway; i.e. cast feather fall).