*DISCLAIMER* This info is to the best of my knowledge and from what I saw testing one of my lipos. you're mileage my vary
Ok, While I've never owned a multi cell lipo without a balance plug I am somewhat familiar with the PCM boards inside lipo packs. So, I did some reading on the PCMs, lipos without balance connectors, and specifically how to charge them. There should be a lipo charge setting on your lipo charger that will charge a lipo without the balance plug. I dont know exactly what it will be called on your charger but on my Hitec X700 its just called "CHARGE" as opposed to "BALANCE" that I normally use for balance charging. (This is the first time I've ever actually used the "CHARGE" option) Use that charge setting at 1C and the internal PCM boards will keep the individual cells from over charging. I just got done testing it with a random 2S pack that I picked up off of my shelf and once the charging cycle was completed without using the balance plug both cells were within .003V of each other. 4.194V & 4.197V respectively. doesn't get much closer than that. So it should be perfectly safe to charge that way.
I appreciate you showing us the internal composition of that pack. I hope you have some shrink wrap laying around to re-do the pack