I have the 405 on my daily carry 638. While I love the Magna/BK grip adapter setup (I do make the BK adapters, after all) there's just no way to beat the accuracy advantage of the laser grip if the S ever actually hits the F. Compared to the Magna wooden grips, the thickest part of a 405 is the slight "palm swell" in the middle of the grip, and that part is nearly 1/8" thinner than a Magna grip measured at its grip screw. Every other part of the 405 is even thinner (except for the laser bump, of course, but I think all the laser grips have the same size laser bump.)
I've never heard a Magna grip described as fat, or hard to conceal. A 405 will conceal even more easily. If you think you need something even thinner than a 405 in order to conceal it, I'd look first at your concealment procedures (cover garments) and equipment (belt/holster.)
I use either a Kholster or SideGuard IWB holster on a Wilderness Instructor belt. I normally wear a sweater as a concealment cover in the cooler months, and a Hawaiian shirt when it's hot. The rubber on a 405 grip does not cling to either of these after you've done some shooting and the rubber has had some sweat and hand oil worked into it.
As for comfort, there IS a cushion at the top of a 405 grip, but I still do NOT find an Airweight 38 comfortable to shoot very much with 'em. I can only handle about 10 +P carry loads at a range session, and even with my powderpuff cowboy loads the combination of light weight and thin grip get to me pretty quickly (a few dozen rounds.) In contrast, I can shoot many dozens of rounds from an Airweight 38 with a Pachmayr Compac or Decelerator grip, and can shoot a steel J frame all day with either of those grips. (The "problem" with the 405 grip is that it's really thin - at the top of the backstrap, the part that puts the recoil into the web of your hand between thumb and index finger. Compared to a Magna grip the 405 is a full 0.140 thinner - 0.86" compared to 1.00" for the Magna. Even with a cushion that's concentrating the recoil into a 14% narrower area of your hand.)
YMMV, of course - my bones and joints are getting old - but if you plan to do any real shooting with your Airweight (which you SHOULD - regularly) then I would absolutely pick the more comfortable grip. If the 405 has some cushion and the 105 doesn't, I would strongly recommend the 405. (Personally, I'm thinking hard about going to a 305, as it looks to be even wider than the 405, and so should offer more area to spread the recoil over. It's a pinky finger longer, but I would work out a different gun location and/or cant angle to hide that extra length if it meant I could shoot the gun more at a practice session.)
Let me also add a recent laser grip experience, that relates to any grip you finally choose to carry. If you can possibly do it, find a way to COMPETE with that laser grip. I'd been practicing with the 405 for more than a year, every time I went to a range session, but it was always solo practice - it was in a police training bay where I could draw and move, but always alone and on static targets on standard frames. But a few weeks ago our range did a quasi-IDPA match that was "shoot what you carry," with 5-round strings and reloads off the clock - IOW, a J-frame friendly match. Now I've been shooting IDPA matches every month for several years (mostly with Glocks) so I'm accustomed to the process and the scenarios. Despite my practice experience with the laser, during the first couple of stages I found that I was just using the iron sights on the 638 - although I was noticing that the red dot was out there, I just wasn't focusing on it as the aiming device. But by the end of the match, I WAS using the dot and not the irons - AND, it felt like it was faster to get on target, and I KNOW I was more confident of the shot placement with the laser at the time the hammer dropped. Without the (little bit of) pressure from the clock and the spectators I don't think I would have made the transition to relying on the laser in a hurry-up situation.
So I'd encourage looking for a match or two where you can shoot with your carry gun and laser sight. Lasers aren't allowed in sanctioned matches, and a J frame is at a real disadvantage when stages are mostly designed for 10+ magazine capacities. But some clubs will be more accommodating if you tell 'em why you want to shoot your carry rig - you won't be eligible for a trophy, but that's not what you're there for.