You can make the process safe, by taking great care in the job.  It's not inherently safe.

You can't fully discharge a LiPo and have it be useful -- a LiPo will still deliver current well past the point where it is permanently damaged.  So you can't render it safe by discharging.  I suspect you can render it safeer, but I'm not sure it's worth it.

Get everything lined up.  Remove one and only one wire from the old connector (or cut it and strip it to splice onto the new -- whatever).  Get that one wire installed on the new connector so that it cannot short out to anything.  Repeat the process one wire at a time until you're done.

If you're worried, have a metal or pottery container handy to brush the battery into -- LiPo cells don't burst into flame reliably enough to be a weapon, but they have their own fuel and oxidant in the same package, so when they do burst into flame you can't put them out -- you can only wait them out, and you can only do that if you can isolate them from anything flammable.

Discharging by running down on the plane is static condition is not great.  There is not good airflow, so heat, and amp draw will be higher, though you can control that with a prop change.  Some ideas here

https://stunthanger.com/smf/gettin-all-amp'ed-up!/battery-discharger/

either a bad board (it was new) or I put a 4s into a 5s slot or put it backwards.

I don't think a battery charger would work if any of the wires in the balancing plug were swapped.  I looked at all of my batteries balancing plugs.  With the balancing plug laying so that you can see the contacts the black wire is on the right.  This wire is always the negative side of cell #1.  From there the next 4 wires are cells 1 through 4. A note of interest is that their was not a standard color code to indicate cell number.  Having said that the cells always cane in sequence from right to left and the black wire was always ground (or negative) for cell one.  So you can place the negative lead of a digital volt meter on the black lead (lead on the right) and measure the other leads from right to left.  On the battery in the picture I measured as follows: First to second lead 3.73V, first the third lead 8.01V, first to forth lead 12.02 volts, and first to 5th lead 16.36V.  The polarity on the meter always showed positive voltage.  In fact you can measure the voltage of each cell individually.  1&2 is cell #1. 2&3 is cell #2, 3&4 is cell #3, and 4&5 is cell #4.  So anyway, if any of the wires were swapped in the balance plug a charger, that is worth having, will reject a miss wired plug.  Photo attached of the plug I am talking about.

First and last give total voltage and internally are on the red and black leads.  Each wire matters for balance and gives cell to cell voltage.  Take a volt meter and put black on black or the balance lead and then walk across the colors with the red meter lead and you see a cell added with each move if the wires are in order. Or move both meter leads and read the cell to cell to cell voltage.

If I have to change plugs, to a different manufacturer,  I do one at a time and realize that colors may not match but order has to match, and has to match the plug direction.  You could get a plug with different color end leads.  Look at plug polarity, not colors.