To me this sounds like contract manufacturing, rather than outsourced processing.
Definition of outsourced processing from the glossary: Where an intermediate production process or step in the manufacture of a product is completed at another company or site.
And more detailed blurb from the into to section 3.5.4 in the Issue7/8 guide to changes:
Outsourced or subcontracted processes occur when a partially processed product is sent to another site for a process step(s) before being returned to the site for completion of the production/packing operation.It is vital that the site manages this process to ensure that product safety is maintained and that customers have visibility of these activities when they occur.Packing of products by third parties (e.g. contract packing) has been removed from this section as this should not form part of the scope of the audit (the packing site is encouraged to have its own certification).
Your example sounds like your proposed subcontractor will effectively be undertaking the entire manufacturing process?
In this case, I suspect the only potential option to include it in your scope would be under section 9, traded goods (although I'd double-check that with your certification body just in case). If that option is viable, you then have the same potential approval routes in 9.1.2 that you do in 126.96.36.199, i.e. GFSI-benchmarked certification, audit, or questionnaire for "low risk" options. If this is going to be your only traded goods/subcontracted manufacturing source then you should probably expect it to get lots of scrutiny during your BRC audit
Even with several hundred suppliers it is often the non-GFSI ones that attract most attention, and arguably this is very reasonable. They certainly are permissible, hence the provisions for them in the standard, but you've got more of a challenge showing the auditor that they're suitable. Aside from the BRC headache, for your own peace of mind you'll also want to make sure you're happy with them - I've seen some very excellent non-GFSI sites, and I've seen others where the audit was abandoned after ten minutes because they were so obviously hopeless. You definitely don't want your brand name and reputation on products coming from the latter!
I think your approach of a physical audit is therefore probably sensible.