3/16 kunifer pipe is what you need, you will get a little bit firmer pedal with braided hoses but if you are working round all your pipes I’d just consider replacing the flexi pipes with like for like and doing a full fluid swap. Also worth taking out your pads, giving them a clean up and refitting helps them slide in the calipers better and firms the pedal
A tip for removing your old metal pipe unions is to just cut the pipe with snips and use a socket with some vice grips on the flexi, just add the union length and 3ishmm on to the new pipe for the flare. You can use a little gentle heat, wire brush and some penetrating fluid on the metal pipe union if you are just doing a flexi, make sure it’s the correct flexi first and you can cut it and turn it if the metal union is seized to the metal pipe, watch it for twisting and you’ll know!