Much easier and more precise method than doing it on rabbits. Won't take as much time.
Go to Abyssea and grab cruor buffs to ensure capped dDEX, also make sure that you have capped crit rate merits. Having a Rancor Collar will also be a very big asset.
Procedure is simple. You use varying amounts of crit rate to determine the crit rate of the weaponskill. Start at 60% (dDEX + Merits + Gnarled Horn + Scorpion Queen + Rancor Collar), find a monster family that is rarely killed and go fight them. Get the monster down low enough so that only one hit of the weaponskill will hit, 5~7% should suffice. Record the damage and do it several more times, a critical hit should be very noticeable especially in abyssea, when you do not see a crit you know that the crit rate is not at the value that you're currently testing at. Move up in increments of 5% crit rate until you do not see any non-crits and get a decent dample size (80-100 weaponskills leaves under a 3% chance of the event occuring). Also make sure that you make note of the TP return of the weaponskill. Any variation in your TP return indicates that you either missed the first hit of the WS or more than one hit landed. Ignore these results. You'll want to do these tests for 100% TP, 200% TP and 300% TP.
In case that was confusing: 60% critical hit rate, fighting turtles in Abyssea - Tahrongi. You have 20% from dDEX, 5% from merits, 20% from Gnarled Horn, 10% from Scorpion Queen, 5% from Rancor COllar = 60%. You do 3 weaponskills at 100TP and they all crit, but the fourth does not. You've determined that Drakesbane's crit rate at 100% TP is not 40%. Move on to 65% crit rate and repeat.
This is how I tested for Chant du Cygne's critical hit rate. Values will be nearly precise for these tests.
Link to my testing for reference:
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