Mob Spawner that was blown up by a creeper is no longer working

That sounds like a bug. Check to see if it's reported on https://bugs.mojang.com already and if not, report it.

About your question: Since the data in the spawner was deleted, there's no easy way to restore it. You could get a spawn egg out of the Creative mode inventory and apply it to the spawner to make it spawn that entity, but it would likely still not be the same spawner as the one that was originally generated, for example the activation range, the spawn speed and other aspects will likely not be the same.

There is a more simple answer.

In BE spawners will likely drop as an item from creeper explosions. When this happens however, it deletes the previous mob egg within it. This explains why there is no action happening inside the spawner, thus rendering the spawner inactive.

Since your spawner has been deactivated after being placed, you need a way to actually put a spawn egg inside, and you can't do that in vanilla survival.

So it's better having cheats on to put back the skeleton inside, but if you really want to keep it vanilla (for some reason, mine would be for achievements), then this isn't possible.