The same way you would get it directly to Sheffield within the same time frame without sending it to him first:
You overnight it to him in the UK using either DHL or UPS, including the return international waybill information.
He gets it the next day, adds his documents and then mails it on to Sheffield to arrive the day after.... If he's organised, you could get it to Sheffield from the US in as little as 48-72 hours.
If you actually want your documents to make it to Sheffield, you should not be using any other mailing service than DHL or UPS, preferably next day (I would expect to pay about $100-200 each way for postage). Don't use FedEx because UKVI will no longer return visas through FedEx.
USPS is unreliable and your documents could take weeks to arrive (or may never arrive) as they may get stuck in customs. I would only ever use a tracked l, fast courier service to mail important documents.
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