Really depends on the type of product and the standard within that industry. As an example, furniture items can take months to deliver. On the other hand, if you're drop shipping, and customers can get the product cheaper and faster from somewhere like Amazon you may have some challenges. The key in dropshipping is to distinguish yourself from an authoritative, content or other standpoint so that customers are willing to sacrifice cost or delivery efficiency for the security your "brand" represents.

If you tell them upfront, yes. Depending on your shopping cart, you might be able to price and name different options. This will clearly indicate the amount of time.

If you disclose up front that you are going to have an 8-10 day deliver time, then your customers will make their buying decisions with full information weighed in.

Communication with your prospects is key to ensuring that you don't have disgruntled customers creating viral negativity towards your business.

Give your customers a choice and let them decide price vs speed as long as you feel the 'value' equation works and isn't "are you kidding me" at the fast end as that can drag down your whole brand.
Then on the longer delivery, be very very very clear upfront pre-purchase both the time window and why (your value to them) and perhaps a few alternatives that reduces time (even if few days it gives customers choice and shows your 8-10 value). Also OVER communicate with simple clear email that show where their order is in the process and time left.. otherwise you'll be hit with lots of customer calls and potential cancelations.
Set your value, add choice that can also show your value, over communicate preorder and after order.