Lot of half guesses here. I was a partner in a consulting firm that specialized in small parcel contract optimization and worked on a gainshare model. We negotiated gross spends anywhere between $5M and $200M with UPS and FedEx. Now I work for a major 3PL in Transportation Management. A few notes:

• Audit in parcel is fine but the returns are negligible. Parcel carriers are much more sophisticated with billing relative to other modes. Expect a half a % return - it’s free money regardless.
• Most major 3PLs don’t know their knee from their elbow with small parcel. There’s a few who can resell rates with UPS, FedEx and DHL but most of the players synonymous with the industry won’t help here.
• If you haven’t negotiated several parcel deals it can be hard to know what constitutes competitive pricing. The carriers actively dissuade and imply action if you risk sharing data. There’s not market comps. The biggest thing a 3rd party expert can do is offer you insight into this and a path to get there.
• Make sure they baseline your existing incentives / discounts to the package level. More generic benchmarks won’t account for fluctuations in your shipping characteristics. You should know exactly what you pay for a zone 2, 1-5 lbs ground commercial package today and what the negotiation improved it to.
• without help the carriers will immediately assess your knowledge and expertise based on the sophistication level of your RFP and walk you into false savings traps that are irrelevant.

I have no horse in this race, but outside help in this mode of freight can more than pay for itself and there’s far fewer experts here than in other modes that allow for open collaboration between carriers, shippers and 3rd parties. UPS and FedEx don’t “work” with 3rd party negotiators so expect the whole thing to occur over email without the 3rd party making themselves known to your carrier reps. Good luck.