Wood, 31, hit the headlines after having a testicle removed following the defeat to Leeds, and his personal life has also been subject to much scrutiny by the national press in the close season.
He will now turn out for the Lions against Workington this weekend, as part of the partnership they have with Warrington.
The Wigan-born prop has made nearly 300 appearances for the Wolves since he made his debut in 2000.
Swinton's opponents Workington are likely to have a couple of players from Widnes featuring in their line-up - the Vikings have confirmed Declan Hulme will definitely feature for the Cumbrians.
This epic clash will be the last time that Rhinos' rugged veterans Jamie Peacock, Kylie Leuluai and Kevin Sinfield will wear the Leeds colours, and they will be keen to end their playing careers on a high.
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