Strip about 3/4 to 1" back on each wire.
Add 1" piece of self gluing heat shrink tubing to one end.
Fan the ends of both wires.
Wrap each end around the opposite wire.
Tug gently to seat.
Cover with heat shrink and heat it.
No solder necessary.
Alternatively, use heat shrinkable butt connectors sized to the larger wire, and strip double the length on the smaller wire and fold it back on itself.
Heat and shrink the covering to seal.