You should be able to transfer the files without having the program available. That's the same as transferring an mp3-file you downloaded without having a program to make mp3's. It just are files on your hard disk that you can copy to everywhere you like.

Assuming these files are important enough for you to backup and the backup program you used you might be able to get them from your backup also.
Not having a backup implies you didn't mind to lose them. So why mind about copying them then?

Kees