The yarn recommends a 5mm needle so going up in size is helpful. However, the best way to tell about drape and feel of the knit piece is to work a good-sized swatch. It will take a minimum of time and effort but be worth it to get the needle size you need and the feel you prefer, not too loose or too tight.
What sort of border does the pattern have? Is it something that can be left off for the time being and returned to at the end perhaps?
I sometimes skip the bottom rib on a sweater and return to it so i can decide on the needle size and type of hem i want later on, it’s also easier to redo it if its added later.
Having said that i tend to spend extra time deciding on the hem/border before setting off on cables because I prefer cables to run out of the hem with a flowing knit column that’s uninterrupted.
Using a larger needle is quite common for me, I prefer the drape so i think if you like the cables on 6.5 mm then go for it.
If you have already cast on a lot of stitches and worked the border on 6 mm you could work just a section of the 6.5 mm cable part back and forth leaving the other stitches on hold, like a test section, and see if the 2 sizes work together. It would have to be undone to be able to work the full blanket of course but it might help you decide what to go with.