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.