Hi and welcome. Where to begin... Ok, you've been hearing some good advice. In many cases, the ridiculously large watt factors on many mods are hype and nothing more. They can't really attain them or at best momentarily. And yes, there is a difference between amps and watts; the rule of thumb you were given is a good one. If you have an 18650 rated at 20A CDR, you can safely get 60 watts our of it.
Oddly enough, the board in Panzer-- advertised as a true DNA200-- is one of those which can make its rated wattage. Therefore the selection of the LiPo replacement is going to be critical. A DNA board requires a 3S cell-- a 3S LiPo is usually just three 1S LiPo cells wired in series and shrink-wrapped together-- of sufficient current capacity to support the board's draw. Details for the battery spec can be found on Evolv's website. If you can get the mod open, there's probably a manufacturer's name and part number on the battery pack; Google is your friend on that. A direct 1:1 replacement would probably be best, especially is the pack comes with a connector of some sort, of which there are several in common currency. If the pack will require a soldered connection, and especially if the connections will have to be made to the cell tabs themselves, either to connect the pack or to build the pack before connection, do not try to do this yourself without a good bit of practical knowledge of electronics. If you overheat that tab, you're in for some fireworks. Neither is just taping a too-large LiPo pack to the back a good idea. The charging board is almost certainly built for the 4500 mAh cell the mod comes with, and will balance charge it nicely (or not, that might be why the LiPo went south). Lengthening the leads to get the pack outside the case is not a good idea either. LiPos are safe enough if used in their designed manner. But designing a manner in which they might be safely used is a job for somebody with a lot of knowledge of electronics, not a casual user.
If you know what you're doing in electronics, fine: have at you and good luck. But the title of your thread is "I don't want to die." If you don't, remember the proverb beginning with "a little knowledge..." and stay away from repairing a LiPo mod unless the cell replacement is a 1:1 match with a connector you can just plug in. I know you say you can't afford a new mod, and believe me when I say I've been there. But you'd do better selling the board in the Panzer to a modder who knew what they're doing-- DNA200s are expensive-- and buying a smaller mod with the money.
Good luck, welcome to the board, and try to stick around a while.