Am I being unreasonable for wanting another one sent?

Yes and No.

As a seller if I feel a replacement has the possibility of also being lost then I will give the buyer a refund.  It's a seller's prerogative to do so as long as the result for the buyer is that they are not out of pocket for the transaction.

As a buyer I can understand that the China seller is sending a sooper dooper cheap as chips product so of course you would rather get a replacement than have to source a (possibly) more expensive product elsewhere.

At the end of the day, though, you said yourself that the item's only $1.98

Seriously.. I'd just take the refund rather than push a point over a transaction worth less than $2