Using compare.irowiki.org, it looks to me like you'll get a lot more mileage out of a properly rolled Katar [2]. ASPD +2, Crit Damage, and Crit Rate options all give more damage on the Katar in every calculation I've done.
That being said, while the DPS difference is significant (10~20%, roughly), it relies on getting a decent roll on your second line of the Katar. You'll still get perfectly respectable damage on the Jur, so if you want to skip that RNG hell, you'll be more than fine.
This also assumes you can get your crit rate high enough that you don't need to use Soldier Skeleton cards at all. Personally, I think the card is awful, so I avoid it like the plague. 2x Kobold + Hair Brush + a decent amount of Luck will give you a good chunk of crit rate on its own. You can make up the rest right now with a Green Maiden card if you're rich (if you're planning on using The Paper cards, I assume you're making money somehow), or be patient and wait for Fever Fields to get some Crit Shoes.
If you're using The Paper cards, Crit rate enchants will give you more DPS than ASPD +2 as well, assuming you don't have over 100 crit. But with Fever Field shoes giving a potential 20 crit (40 for Katars), getting over 100 should be hilariously easy, so in the long run ASPD will probably give you more mileage.