Does a minimal difference in hook sizes really change the outcome of a project?
You'll probably be fine. One quarter of a millimeter isn't a huge difference, particularly considering how large the hook is.

The reality is that the hook size is just a suggestion. Different crocheters will need to use different hook sizes depending on their tension. Someone who crochets very loose will need to use a smaller hook for the same project while someone who crochets tight will need to use a larger one.

Assessing gauge is necessary when starting many projects. Some are pickier than others. A shawl/blanket/scarf is unlikely to need you to find your gauge first as you're not working to size anything. Hook size and yarn weight is much more flexible in these projects. On the other hand, clothing (like a sweater) will require you to use the proper gauge for you to get the item sized properly. 

If gauge matters for this project, work a test swatch using your hook and compare it to the recommended size. If your pattern says that 8 stitches is an inch and your test swatch gets only 7 stitches to the inch, you need a smaller hook. If, however, you get 9 stitches, you'll need a bigger hook.