If you have the correct sizes, Sharkbite fittings are able to transition between materials like copper and pex as long as you use the correct liners/pipe stiffeners in the plastic ends. Bear in mind if the copper tube is acting as part of the electrical earthing, you should add in an earth bond cable between the two sides to bypass the plastic section. This may be totally unnecessary but it's something to be aware of none the less.
No reason why you can't cut out the valve and bridge the gap with pex and pushfit if the valve is truly redundant. Just follow the manufacturer's instructions for the fittings and you'll be fine.