You can create a customer account for yourself and give it an “admin” tag. Then check for the tag in your theme code to insert the Edit link. The following code can be inserted where you want the link to appear, in your product page Liquid file (product.liquid, product-template.liquid, etc.).
{% if customer and customer.tags contains 'admin' %}
Edit Product
{% endif %}
When you are logged in to your own customer account, you will see the link. Others will not see this link, whether they are logged in or visiting as a guest.
See here for more details: https://community.shopify.com/c/Shopify-Design/Creating-an-Edit-Link-in-the-Product-template/m-p/175529/highlight/true#M49586
Note: target=“_blank” will force the link to open in a new tab. That way you can close the tab when you’re done saving changes and go back to the website. If you want it to open in the same tab, just remove this code.