With Site Properties you mean the SPSite.RootWeb.AllProperties
property bag which you have filled with some custom property?
Assuming that is what you are talking about, there are unfortunately no standard ways to work with property bags - besides programming that is.
You said you want to set a default value on a list field for each list item. This sounds like an event receiver! You can choose to have it fire on item updating and/or item created for all your items and always set the hidden field on the item with the value from the site properties.