Would vs Should - a question of certainty

[endolin]

In the following paragraph extracted from a news article, I was wondering if the word "would" also indicates a higher degree of certaintly than "should".

At 12.30am, I sent an email to the Swissport lost property office, convinced I would never see the bracelet again. Seventeen minutes later, a brisk missive appeared, headed "The George Bernard Shaw bracelet" (rather than the Oscar Wilde earrings, or the Leo Tolstoy necklace). It informed me that my lost property had been found and would be dispatched the following morning. It would arrive (not should, but would) in three to four working days.

[Alan]

Yes, I would say so!