If I had to lay it per 'Mech, I'd go with the following:
Fire Moth: Spider -- Spindly legs and body shape
Mist Lynx: Commando -- That's about as close as I can think of; there's not a lot of IS 'Mechs of the age that have wrist-mounted missile pods
Kit Fox: Jenner -- They share a same general shape, with chicken legs, a thrust-forward cockpit, and a sort of hood rising from behind the head, though the warbook would probably have an issue with the Fox's arms
Adder: Jenner -- For much the same reasons as the Kit Fox
Viper: Raven -- Chicken legs and a prominent beak, though again the difference in arms is going to give the computer fits
Ice Ferret: Assassin -- This is a bit of a stretch, but they're both man-walkers at least. Neither one has a a humanoid head that sits on "shoulders," instead having a cockpit that thrusts out from the front of the torso
Nova: Crab -- Also not a decent match, but they're both chicken walkers with outward-thrust cockpits and prominent arms
Stormcrow: Jenner -- Another issue of arms, but the combination of chicken legs with an outward-thrust cockpit beneath a missile bank is too close a match
Mad Dog: Cataphract/Caesar -- There is no good match for this one, mostly because chicken walkers appear to much more common among the Clans than they are in the Inner Sphere. The Cataphract and Caesar at least have the right legs and a fairly prominent center-line.
Hellbringer: Warhammer -- This one seems a little obvious to me, what with the shoulder-mounted missile launcher and searchlight combined with man-legs and a fairly squared-off torso
Summoner: Thunderbolt -- It's the missile launcher and the off-center cockpit that make this one for me, just too much similarity there
Timber Wolf: Catapult/Marauder -- We all know that one
Gargoyle: Atlas -- Angry face, rounded top, and man legs
Warhawk: King Crab -- These two share a weight class (and thus are of a size), leg structure, and hand-less arms with a superstructure above & behind the cockpit. It's not a great fit, but it's about as close as I could come up with
Executioner: Banshee -- Another angry face, but this time with a squared off top instead of a rounded top
Dire Wolf: King Crab -- See: Warhawk.