As long as the Bills make him an offer, if another team signs him we would get two 1st rd picks. No other team would give up that much for him so a trade , resign with the Bills, or tag. So I think a trade is ok if he will not sign his tag.
In 09 NE tagged Matt Cassel for $14 M , he signed, was traded with LB Vrabel to KC for a 2nd rd pick. KC negotiated a 6 yr $62.7M contract for Matt. Until Byrd signs the tag he can see what other teams will pay him and if the Bills will accept the trade offer or keep the tag on him.