Murray has hired the Frenchwoman initially for the grass-court season but both have already stated their intention to work together for longer.
Mauresmo has so far been even more of a high-profile appointment than her predecessor Ivan Lendl, who guided Murray to his first two grand slam titles in their two and a half years together.
It was Lendl who ended the partnership in March, with both men having previously expressed their hope that they might work together for the rest of Murray's career.
In the end Lendl decided he no longer wanted to commit the necessary time to the arrangement, a decision that initially hit Murray hard.
HSBC Ambassador Henman said: "I think it's certainly an interesting choice.
"I think the timing of it is not that straightforward, coming in at this time of year, trying to build that relationship when the eyes of the world are on them both.
"But I certainly do hope it works, because the continuity for him is really important, so I think they should stick together for a good while now.
"Chopping and changing I don't think is so good for him in the long-run, so fingers crossed it works out well."
Murray's decision to choose a female coach, the highest-profile male player ever to do so, has been the talk of tennis over the past two weeks.
Most people have been positive about the appointment but there have been dissenters, most notably fellow former Wimbledon champion Virginia Wade.
"The only things he can control are preparation and performance," said Henman.
"What's been talked about in the press, on the television and radio, people's opinions on his new coach, he can't control that, so there's no point in worrying about that.
"Coming back as defending champion, it's massively exciting for everyone.
"I think the draw's been favourable to him, there are a few tricky ones out there, but on the whole he's got a pretty good section.
"But again that means nothing - he's got to go out and earn that favourable draw. He was able to do that last year and hopefully he can get on a roll again this year."
On appointing Mauresmo, Murray stressed her ability to listen as a key factor as well as the Frenchwoman's calm presence and experience.
"The stuff we've done on the court hasn't been that dissimilar in terms of the practices and the preparations," he said when asked to compare Mauresmo and Lendl.
"The way they speak to you is different, that's for sure. They're completely different people, completely different personalities. They both come from different parts of the world. They have different upbringings.
"But the key to good coaching - there could be 100 coaches that might be trying to get me to do the same thing, but it's about how you say it. That comes through communication. Not everyone has that skill. Some people do.
"I'm not going to work well with every single coach or every single person. It needs to be the right personality fit. I hope I found that."
Murray began the defence of his title in convincing style with a straight-sets win over Belgian David Goffin and next meets Slovenian left-hander Blaz Rola.
Rola has lost twice in recent weeks to British number three James Ward but has never previously played Murray, who practised with left-handed doubles specialist Mariusz Fyrstenberg on Tuesday.
"I don't know loads about him but I watched him play at the French Open," said Murray of Rola. "James Ward played him in the last round of qualifying there.
"I know one of the British guys also played him in the qualifying at Eastbourne last week. So I know a bit about him.
"But he hasn't been on tour too long. So I'll watch a little bit of video of him and get a better idea of his game."
Rola, 23, only began playing on the tour full-time this season after studying at university in America and broke into the top 100 for the first time last month.
The Slovenian cited playing Ward at Queen's two weeks ago as his biggest match before Wimbledon and the prize of playing the home champion gave him an extra incentive in his first-round match against Pablo Andujar.
"When I saw the draw, when I saw that potentially I can play the second round against Andy, my motivation was off the charts," he said. "It helped me a lot.
"I'm very, very happy that I actually get a chance to play him, especially here. I think it's going to be a lot of fun."