Again, not perfectly clear which battery are you talking about? It sounds like you are using the 18350 in a Mini Provari. You only said Provari in your original post.
I have never heard of a Squire mod, and could not even find it on Google. Can you post a link?
One can't say with any certainy whether a mod will require a flat top or button top battery, or maybe it won't matter which one...it just depends upon the specific mod. Again, a link to what you are looking at would be a huge help.
The Smoktech Gripper is a small mechanical mod that uses an 18350 battery. I use mine to stealth vape at the cinema. I use the same AW 18350 imr button top battery in this as my Mini Provari. The Gripper is only $16 so if it gets stolen you are not out much money. Don't let the inexpensive price turn you off from this mod; it's made of impact resistant plastic and is a tough little mod that could take some abuse. If you decide to get one, be sure to get the extension ($4) so that you can put another type of juice delivery device on the Gripper other than the XL cartomizer that fits inside the Gripper's body.
You can purchase this from either Got Vapes or Mad Vapes.



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Edit to this post: I finally located a vendor for the Squire 18350 at Smoke Revolt.
http://www.smokerevolt.com/18350MiniTube
Mechanical mod, can't beat the sale price of $15. Looks much like a Puresmoke Mini Legacy. A user comment on this site stated that a flat topped 18350 battery rattled a little bit, so perhaps a nipple/button top battery would eliminate this. If not, stretching the hot spring might also eliminate the rattling.