Help How do I wipe device that has only 2% battery?

Iif the charging port is bad the repair shop will probably replace the motherboard so the NAND Flash chip (the internal storage memory) will get scrapped as it's physically part of the logic board itself, or just as likely the phone will just be scrapped and/or disassembled for parts. Profit margins aren't very much for brand new phones, so spending money to repair a rejected/damaged phone is a profit loss. Phone repairs are done because of warranty obligations or the buyer paying for it. But even in the event your old phone will be repaired keep mind most smartphone internal components aren't very modular and are not readily replaceable individually. So if one part goes bad, it's easier to swap the entire board -- de-soldering individual parts and re-soldering replacements requires a lot of time, effort, and when it involves items like microprocessor parts, specialized equipment. So even if the wipe is never done, your data isn't retrievable anyway (new mobo, new internal storage). But don't forget to remove your SIM card and your microSD card.
Of course this is dependent on if the charging port is bad. If it problem is actually just a software issue, or something to do with the USB cable or the power adapter, than that changes everything. How did you determine the charging port itself is the problem?

Keep in mind that once you do send this phone back, even if there is no screen lock and some tech staffer starts it up, the phone won't have any online access to receive the remote wipe signal anyway. With no SIM it won't have any cellular connectivity and with none of the saved WiFi networks you added being out of range it won't have any WiFi connectivity -- unless you had it set to automatically access any available open (no password) WiFi network (or you have something like Comcast's privacy-riddled public Xfinity WiFi network at home and this service shop is also using Comcast for broadband). But again, this is all just supposition, the odds are the phone gets scrapped, there's no profit margin in repairing it.
But your description on the charging problem 'could' be due to the USB cable you're using. The plug on the end of the USB cable is held in place simply by friction fit so it's a matter of tolerances -- if the crimp in that metal sleeve in the plug isn't making enough physical contact with the metal sides of port in the phone, the plug won't be firmly held in place (the metal contacts in the plug can't transfer power to the metal contacts in the port). Have you tried a using a different USB cable? This won't make any difference if the problem is with the port in the phone of course (e.g. a bad solder joint that connects the port's internal metal contacts to the motherboard). If a different cable does work, this might at least be enough for you to charge the phone so you can copy off any data you need and do a Factory Reset.