You will definitely have to decrease the number of stitches with the bigger yarn/bigger needles, I think.
After your first rows of fun fur you will have to change needle size and yarn for the bulky main pattern stitch. The first row with the new yarn / new needles I would knit 2 together of the old yarn into the new yarn.
To be safe, don’t cut the fun fur yet when you do this. Instead knit a couple of rows with the new yarn and see if the transition looks right. I.e. the scarf stays the same width through the transition. If it doesn’t look right you can rip it back out and to more or less decreases.
Alternatively you could make a swatch with the fun fur and see how many stitches per inch you get, determine how many stitches you need for the planned width of the scarf and then you can do this exactly.
Hope it works out! Good luck and let us see the FO when you’re done.