Henry completed a £16million switch to the Nou Camp on Monday, 12 months after spurning the Catalan club in favour of remaining with the Gunners.
The France striker decided to move on this week, though, and revealed the situation at the club following vice-chairman David Dein's departure last season, and the apparent uncertainty over Wenger's future as manager, were reasons behind his decision.
Hill-Wood, however, told the Daily Telegraph: "I am not particularly worried about what Thierry said but whether it really influenced his decision or not we will have to wait and see.
"We certainly don't think Thierry Henry going and Arsene Wenger's contract situation are in any way linked. That was just an excuse."
Wenger, who has a year remaining on his contract, continues to be linked with a move away from the Emirates Stadium - with Barcelona the club most regularly linked - but Hill-Wood hopes the French coach will remain in north London, even if he does not sign a new deal this summer.
"I am really hopeful he will extend but at this moment I am only in a position of hoping," said Hill-Wood. "I've no reason to think that he won't but at the same time I have no reason to believe he will say yes. Certainly we would like to see him sign a new contract - we have made no secret about that.
"But we have not talked any details about anything with him or the board. We will wait and see what he wants to do. Then we can sit down and discuss things if he is positive about it. I am very relaxed. We are in good shape."
Hill-Wood, who also said Arsenal "would like to find another player or two" in the transfer market, revealed he has not met with American tycoon Stan Kroenke since their meeting in New York recently.
Kroenke has a 12.19% stake in the club and is expected to mount a full takeover bid but that prospect is another area of uncertainty.
"I have not heard anything further from him [Kroenke] since we met," said Hill-Wood.