Assuming you enter Lavender Rival in Growlithe kill range (7 HP or less):

CURRENT STRAT
- Standard shopping and Fly menu
- Rival: X Acc, Drill x5 (36.6 seconds if you win; 37.5% chance of winning)

PROPOSED STRAT
- Buy one fewer X Accuracy
- Fly menu: Teach IB instead of Drill. Then teach RS in slot 1
- Rival: IB, TB, RS x2, IB (37.5 seconds if you win; 56.5% chance of winning. Ivysaur is a 68% range)
- Have Rock Slide in slot 1 for Gastlies (-0.2s) 
- Use Super Repel + teach Horn Drill over RS after the Gastlies (+1.3s)
- Ice Beam the Zubats and Golbat (-0.2s)
- Move order is back to normal after this

TOTAL TIME LOSS: 1.8 seconds
TOTAL RISK SAVED: 19 percentage points

A third option is to Potion on Pidgeotto, hoping it will hit you into red bar. This is always the slowest and safest option, and it might lose 15+ seconds if Pidgeotto doesn't hit you into red bar. Also, you can still die to the wrong combination of moves/crits.