Rhyperior
Abilities: Lightning Rod, Solid Rock,
Reckless
Physical: Aqua Tail, Avalanche, Body Slam, Brick Break, Crunch, Double Edge, Dragon Rush, Dragon Tail, Drill Run, Earthquake, Facade, Fire Fang, Fire Punch, Focus Punch, Hammer Arm, Ice Fang, Ice Punch, Iron Head, Iron Tail, Megahorn, Outrage, Poison Jab, Power-Up Punch, Return, Rock Blast, Rock Slide, Shadow Claw, Stone Edge, Superpower, Thunder Fang, Thunder Punch
Special: Ancient Power, Blizzard, Dragon Pulse, Earth Power, Fire Blast, Flamethrower, Flash Cannon, Focus Blast, Ice Beam, Surf, Thunder, Thunderbolt
Other: Roar, Rock Polish, Seismic Toss, Stealth Rock, Swords Dance, Toxic
Look at those options! Lightning Rod and Solid Rock are both good abilities. You could get a Gyarados that's immune to Electric while you setup. It lacks reliable recover and supportive options though. But at least you can abuse a RestTalk Suicune with Solid Rock and Roar/Dragon Tail to rack up SR damage.
Mr. Mime
Abilities: Soundproof, Filter,
Technician
Physical: Body Slam, Brick Break, Double Edge, Drain Punch, Facade, Fire Punch, Foul Play, Ice Punch, Return, Zen Headbutt
Special: Dazzling Gleam, Energy Ball, Focus Blast, Grass Knot, Psychic, Psyshock, Shadow Ball, Signal Beam, Thunder, Thunderbolt
Other: Baton Pass, Calm Mind, Confuse Ray, Copycat, Counter, Encore, Light Screen, Magic Coat, Nasty Plot, Reflect, Seismic Toss, Taunt, Thunder Wave, Toxic, Trick
+Technician-boosted Moves:
Fake Out (60)
Power-Up Punch (60)
Hidden Power (90)
Aerial Ace (90)
Charge Beam (75)
Icy Wind (82.5)
Magical Leaf (90)
Round (90)
Thief (90)
If you want a Technician team that doesn't involve Breloom, it's a toss-up between Roserade and Mime. Roserade can set hazards and remove status from teammates, but Mime has Taunt and Encore which makes Natural Cure unnecessary. Filter is generally better than Natural Cure. Mime also has Nasty Plot, Calm Mind, Baton Pass, and better physical options than Roserade (despite the latter getting Swords Dance). Soundproof if you're scared of all the Boombursts.
There are other Technicians with good move pools, but they lack other useful abilities so you'll be stuck with Technician all the time.