Can I hardwire an LED retrofit disk
Those Philips disks you have are designed and tested to work inside a recessed can.  You cannot modify them as you are suggesting.  First, there's just no way to attach them to the junction boxes.  Second, it wouldn't be "legal" to electrical code and it may not be safe.

Your two options are to get a "flush mount" recessed light disk that is made to attach to a junction box or have the boxes replaced with proper recessed light cans.  Even the "flush mount" lights are 3/4" - 1" thick, so if you want a true recessed look, installing cans is your best option.