One thing we run into sometimes in the vessel/tank industry, is that people have an existing item, and want to go back and certify it to meet some standard. Only the standard mandates how it is built, how it is welded, how it is inspected, and there's no way to certify that after it's all been done.
In your case, first question is whether you're responsible for actually determining the adequacy of those existing welds. If so, that might involve some grinding, or taking samples, testing, etc, and could be rather an involved inspection/testing program.
Or if that's beyond the scope of your work, then you can calculate average sizes and go from there, assuming what is there is "good".
The problem with "ugly" welds is that you also don't know how, or how properly, they were welded other than the ugly. If someone's welds look that, they may not know one rod from another, never heard of pre-heat, etc., no telling.