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.
Ireland coach Mark Aston has praised the senior players with whom he worked at the European Championships last year.
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Warrington coach Tony Smith says the Wolves can get better and have yet to hit their peak form.