To get things started, I'd like to do a compare our first unit to their counterpart, since they will probably be facing each other the bulk of the time.
First, let's talk strictly about talent.
Hay is an above average 2nd line LW, while I'd classify Kariya as a weak 1st line LW. Howe is better than Cook by let's say one or two tiers. You've got me beat at both wings, however, Lalonde is significantly better than Barry. As I have said previously, Barry's talent level is that befitting of an average 2nd line C, while Lalonde is that of an average 1st line C. Does the massive difference in talent between Lalonde and Barry make up for the smaller differences between Hay vs Kariya and Howe vs Cook?
As for our 1st pairings, the difference between Stevens and Horton is microscopic, while Lapointe has a small advantage over Stuart.
Now, to matchup related stuff.
Hay will be lining up against Howe. If you haven't read Hay's bio, his defensive play is prominently mentioned. I don't expect Hay to completely shutdown Howe, but he'll at least do a decent job to prevent Howe from completely destroying everyone. In comparison, I would say the matchup between Hay's counterpart at LW and Cook is a significantly bigger mismatch, even though Kariya is better than Hay in a vacuum. At this level, Kariya is a non-factor defensively and he's very soft. This is a recipe for disaster against Cook, who is a top-20 offensive player of all-time, and very physical. At least Howe will be kept somewhat in check by Hay, while Cook will be free of any defensive pressure from the LW position. Also, Cook is decent defensively at this level, and he has the speed to cover Kariya in transition. Combining the above with Cook pounding Kariya in our defensive zone, and Kariya's less than stellar playoff history could mean that Kariya's effectiveness against our first line could be less than optimal. If Kariya is a non-factor offensively, then your line is reduced to 2/3 its strength, since if Kariya isn't scoring, then he's pretty much doing nothing of value. In comparison, if Hay is not scoring, he's at least back-checking and/or doing the little things, so he's not being completely useless.
As for Lalonde vs Barry, this is a good matchup. Barry is respectable defensively, and he's big and strong, which are important attributes to defend against Lalonde. Lalonde is better than Barry offensively, so Barry is going to have to work harder in his defensive zone than Lalonde in his. Naturally, more energy spent defending means less energy available for offense, and this could cut into Barry's offensive value.
My two defenseman are both very big, physical, and both are mobile. I would feel confident with either Horton or Stuart going up against Howe in the corners, in front of the net or in transition. The best way to combat Howe is with sheer physical strength, and both sides of the ice will have two guys that were known for possessing this attribute. Howe probably can not be completely shutdown, but he can be slowed down, and I feel the pairing I've got can reduce Howe's effectiveness by quite a bit. Since both my defenseman are pretty mobile (Stuart moreso than Horton), they will be able to defend against Kariya's speed too.
With all the talk above about the lack of someone keeping Cook in check, you guys have a solid solution on D with Stevens. Stevens vs Cook in the corners, or in front of the net should be a nasty battle. Same goes for Lalonde vs Stevens. One thing that could be worrisome about Cook vs Stevens is Stevens' lack of footspeed. In transition, this could be trouble. At least you guys have Lapointe who's a pretty good skater. Lapointe's pretty tough too, so he doesn't look like he's going to be intimidated.