Yes it will affect your account.
You would receive a late dispatch mark.
The buyer may not like it, but your best bet would be to cancel the order but with the buyer's permission so you can select Buyer requests to cancel as this doesn't affect your selling standard, then relist when you can post your item.
Never list items for sale if you cannot post within your dispatch times, you can use eBay's Time Away feature, this suspends listings for a maximum of 30 days, or I found it best just to end all listings and relist for sale when it's convenient to post. Unsold items remain waiting to be relisted for 90 days max if you're on the Seller Hub.
@copp.rach
