Nice find! Yeah, that staff is indeed a great weapon for a melee wizard. However, the high level requirement just to get that staff (not to mention actually trying to obtain it wherever it drops) is a little challenging. But the weapon can be substituted for toy hammer in early gameplay, so it’s not too big of an issue.
Now then, let’s do a little assuming and some math. Let’s say you take about 150 base DEX by level 220 for crit and the rest of your stats go into INT. You could even do 4:1 ratio instead if you really wanted to.
By 220 you will have around:
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104 points into INT = 205 INT - 425 magic attack.
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425 x 3 (200%) = 1275 damage each hit.
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Add Lv15 swell left arm (154 physical/magic attack) = 425 + 154 = 579 x 3 = 1737 magic attack + 154 physical damage = 1891 x (critical multiplier) = total damage on hit.
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If you have C1/C2 pyro in the build, you would have (without swell left arm) 1275 + 15 + (x)skill scaling = 1290 + (x)skill scaling. With swell left arm you would get 1891 + 15 + (x)skill scaling = 1906 + (x)skill scaling. I don’t know how well enchant fire scales and what or if it actually scales with any stats though. I read on some reddit post that it does but it didn’t specify and said the scaling was bad. Therefore, I wouldn’t recommend enchant fire at all or just take level 5 and go linker instead. Even with the nerfs it still is good.
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If you take C2 thaumaturge and have Lv10 swell left arm (111 physical/magic attack), you would get 425 + 111 = 536 x 3 = 1608 magic attack + 111 physical attack = 1719 x (critical multiplier) = total damage on hit.
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I’m not sure if swell left arm scales with any stats but if it does, you can factor the scaling in there as well (whatever it may be).
So let’s say you just go pure INT. This might actually be better, especially if you decide to take transpose. And that’s another thing, this weapon makes transpose more viable in the melee build. In my thaumaturge build, it wasn’t viable because of the stat distribution I chose.
By 220 you will have around:
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222 points into INT = 436 INT = 656 magic attack.
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656 x 3 (200%) = 1968 damage each hit.
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Add Lv15 swell left arm (154 physical/magic attack) = 656 + 154 = 810 x 3 = 2430 magic attack + 154 physical damage = 2584 x (critical multiplier if any) = total damage on hit.
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If you have C1/C2 pyro in the build, you would have (without swell left arm) 1968 + 15 + (x)skill scaling = 1983 + (x)skill scaling. With swell left arm you would get 2430 + 15 + (x)skill scaling = 2445 + (x)skill scaling.
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If you take C2 thaumaturge and have Lv10 swell left arm (111 physical/magic attack), you would get 656 + 111 = 767 x 3 = 2301 magic attack + 111 physical attack = 2412 x (critical multiplier if any) = total damage on hit.
So in my opinion, just taking C2 thaumaturge would be better as you only sacrifice a few hundred damage at most on each hit in return for utility from say, chronomancer which would even further increase your DPS anyway because of quicken.
It might be even better to not choose chronomancer at all though because if you choose a higher DPS class instead you could get even more DPS from synergizing your skills with your auto attacks instead of being purely auto attack based.
I think I might make a build/guide based around this weapon sometime and incorporate a bit of my melee thaumaturge I already have made into it. Also, I don’t really know how the build would fare against my melee thaumaturge build DPS-wise.
The toy hammer does do a good amount of damage when combined with the pyromancy skills and the huge amount of explosion damage proc’ing every 3 or so auto attacks (which does 1000-2000 damage). And if you think about it, if you do go 4:1 DEX:INT with the staff you might hit 3000-4000 damage roughly every few hits. So yeah, you most likely will do more damage than the toy hammer lol.
This is all just theory crafting but if it works, then it’ll be a lot of fun. Also, sorry for the lengthy reply. 
EDIT: I also forgot to mention that if you choose C3 thaumaturge in this that max swell brain gives you 45 INT which is roughly 104 magic attack plus that extra few hundred damage from max swell left arm.
Edit 2: In addition to the above, I forgot to factor in the magic damage from the staff itself.
