Removing 'local' option from shipping options and add my own

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We are going to deliver products on certain days, wednesday and friday. So we added our own 'local delivery' option that states this, however the old/default 'local' shipping option shows up still. Can i either remove this option, or add our special instructions to the 'local' option?

here is how it shows now:

Shipping method
Choose a shipping method
• Local. Free
• Local delivery
We deliver to your door on Wednesdays between 1pm-4pm and Fridays between 9am-12pm. Purchases made during a delivery window (i.e. 2pm Friday) will likely be delivered during the next delivery window rather than the same day.