This is not an exclusive or. You get both on every critical hit; you don’t have to pick one, and you don’t have to qualify for either. You just get to “deal [any damage that is sneak attack or skirmish] in addition to the damage from your critical hit.” Basically, resolving your critical hit looks like this:
Roll a high enough number to hit and threaten a critical hit
Confirm the critical hit
Decide if sneak attack applies—Telling Blow says it does
Decide if skirmish applies—Telling Blow says it, too, does
Roll your damage, multiplying your damage appropriately (read: not multiplying extra damage dice like those from sneak attack and skirmish)
While reading that “or” as an exclusive or is possible, that reading fails because in such instances, Wizards of the Coast typically explains when or how you have to choose. It would specify if you have to choose on taking the feat, or on dealing the critical hit, or whatever, and it would specify whether or not you can change your choice later. Without this information, reading it as an exclusive-or means the feat is missing necessary information. When two readings are possible, but one of those readings requires additional information that is conspicuously absent, that is very strong evidence that the other one was the one meant.
It’s also just consistent with the English language, and D&D 3.5e rules text generally—“or” is often inclusive, probably more often than not. English relies on context to indicate the difference, and the 3.5e rules text is no exception here. Again, the lack of details about how and when such a choice is made is the context here that suggests that no choice was actually intended at all. We know that Wizards of the Coast knew how to write about mutually-exclusive choices; we have lots of examples of them doing so, talking about how and when the choice is made. There isn’t a whole lot of evidence that they suddenly forgot how to do it for this one feat.
Finally, reading this as an exclusive-or also fails because making it an exclusive or turns a mediocre feat into an absolutely terrible one.
By definition, having both skirmish and sneak attack means multiclassing. Both are inefficient approaches to damage, and they largely interfere with one another. Sneak attack wants you to stay largely in place and flank with someone, skirmish demands you move. Unless you can move from flanking position to flanking position, or move and simultaneously deny your opponent’s Dex to AC, and do all that without giving up your full-attack, you are doing dramatically worse than a rogue or scout typically would be—and those are not high-damage classes in the least. And here you are, investing a feat—an incredibly precious, scarce, and valuable resource!—into critical hits, which happen all-too-rarely, just to try to get around that awkwardness.
A rogue/scout has a lot of difficulties. Trying to build around critical hits has even more difficulties. Making life even more difficult by forcing you to pick one with this feat is simply inappropriate.