What I did is cut off few wires(not cut off the whole wire) so the wires can fit in the connector cups
If you can let the solder melt fast, it would be easier to do. I recommand using leaded solders, and leaded solders melt in relatively lower tempurature than lead free solders, but they are toxic so should be careful when using them. Or you can use a iron with higher power, and it can raise temputure quickly so solders melt quickly.