Not sure why it would take 10 days or more (unless Best Buy is saying that because they are sending it in for you versus you contacting Apple yourself and initiating everything. Or if it’s not in stock which if that’s the case you can’t be upset that they didn’t have one immediately available for you). It’s possible that’s the estimate but it will be faster. Also depends on if it’s including you having to ship that one back first, processing the return and then shipping the replacement. Regardless though…if it’s giving off fumes you all shouldn’t still be handling the device at all. Express replacement service is also an option. Not sure how much it would be if you don’t have AppleCare+ but usually you have to provide a credit card for them to have on file…you may be charged a temporary hold for the retail cost of the device (I say may because I never had the hold occur when I used the service) and the replacement is sent out overnight. You would have up to 10 business days return the defective device or your card would be charged the full retail price of the replacement you received. Also if they inspect the returned item and find that the cause of the damage is not something covered by the manufacturer warranty or AppleCare+ if you have it then you would be charged.
iPhone Express Replacement Service - Apple Support
If you haven’t contacted Apple support directly about the situation outside of the Geek Squad interaction do so and ask if there is a faster option available. Like mentioned though….if you don’t have AppleCare+ it will likely be something you would have to pay for as it would be expedited service. Replacements don’t mean you get expedited shipping even if it’s an inconvenience to wait unfortunately. Or if there is an Apple Store in a drive able distance it might be worth it to go there and get an immediate replacement.