Danmar123 - if the existing lead does not have a ground wire, then do not connect the ground in the new cable - it is designed to work without a ground.
Just make sure the polarity is correct.
Re: insurance - asking an underwriter may get the answer you desire, but they are just offering an opinion. Dealing with the claims officer is a whole different kettle of fish, especially if the fire marshall indicates there may be a problem with the wiring - something to ponder.
Having said that - all of my cables are DIY and I accept responsibility for that. I also ensure they are constructed to the very highest quality levels, grossly over built and any internal connections are identical to those employed by the manufacturer e.g. using identical spring clips or spades or other fastening devices.
Anyone undertaking power related upgrades do so at their own risk. Companies spend lots on UL certification and any kind of power related upgrade can be viewed as negating this certification.
Power cables with IEC/MAINS connectors are purpose built, but many of those on the market are not UL certified, making their use a possible grey area.
I actually purchased one expensive power cable that had the polarity reversed - it went back.
It just boils down to how much risk are you prepared to accept?
Hope that helps
Regards