Proper way of using a Mixing Service
Either of these solutions would work. 

If you mix it first to a previously unused address or send it directly to the merchant via the service (ignoring the issue of timeouts on a merchant terminal if they have such a feature) the effect is the same.

The only thing to make sure is any change does not go back into an address which has not been via a coin sharing service. This will cause a link-back to your previous transactions.

The easiest way to avoid this is to have two separate wallets, one which is only been mixed and one which has not.