In an airdrop, it’s new funds being given to some set of people
Typically funds reserved to holders of an older coin, who can claim a corresponding amount in the new coin, by proving they hold the old coin. Pretty much what you described.
There are other types of airdrops, but what you describe is the most common type.
In this context, the history of previous transactions of the old coin would be irrelevant, unless you want to keep it for archival/historical reasons. Like you said, the actual blockchain can be ditched, since you only care about the balances at the time of the snapshot.