I only have a couple of orders and was recently locked out of my account due to an apparent suspicious login. I couldn't get in at all to ship out an outstanding order, by the time I regained access it was 3 days overdue, I reached out to the buyer apologising for this and got the order out right away but this has now dropped my on time shipping down to 67%
Is there any way for this to not be held towards my stats since I physically couldn't gain access to my account to fulfill this order until etsy gave me access back so this was not my fault?
no
You have much more serious problems than having a late shipment.
My advice would be to contact Etsy and ask them to have a really close look at your shop...
you have bigger worries:
https://www.etsy.com/seller-handbook/article/1075628311049?ref=handbook
Counterfeit or unauthorized items are prohibited on Etsy. We consider counterfeit or unauthorized goods to be items that imitate an authentic good, particularly by using a brand’s name, logo, or protected design without the brand owner’s consent."