Can I change my watch band to the other color after one-day purchase?

In the US you have 14 days to return an item to Apple no questions asked (does not include damage by user) so yes you can change your band by returning to a local Apple Store or beginning a return.

https://www.apple.com/shop/help/returns_refund

If you return to the store, take ID, your receipt and any boxes the item came in.