Almost any bootable backup package will do this for you, because it will treat whatever is on the drive as bytes and not care if they are Windows files, Ubuntu drivers, or pictures of your family.
Until recently, I was using a floppy to boot Norton Ghost 8.0 (the 2003 version). My system is triple-boot, but no Linux (one boot is DOS). I have tested Acronis at work with success, used EASEUS ToDo backup at home with success (but a serious problem - 3.0 backs up but does not restore, 4.0 restores but does not back up). Many people swear by Clonezilla; few swear at it.
I suggest that you get your hands on two extra drives, one external and one internal. Back up the SSD to the external one with the package you are testing. Remove the SSD's cables and install the other drive. Boot to the package, restore to the other drive, and try to boot both OSes. If it works, you have a package that does what you want.