Sticky back would hold the corner.  Just hoop the stabilizer and not the napkin/hanky/cuff/collar or other unhoopable item.

I love your name - pottersclay - that sounds like you are a work in progress and looking forward to wonderful things!

I agree with Pattiann and want to add that you can use another item, heavy tearaway.

One thing I have done is put my napkin in a 5x7" (normally you would use a 4x4) but place the napkin higher than you would normally.  Then use your 'frame' or 'baste' feature on your machine (one of my FAVORITE features), to do a single stitch baste on a square that you have turned 45 degrees.

Leave in the temporary straight pin but stop it short of getting stitched.  The stabilizer should be the proper size for the 5x7" hoop and it is captured in all 4 sides but the napkin is only captured on three.  That is why it needs a temporary straight pin.

The advantage of this method is that, the closer to the edge your design must be, the more obvious it is when the design is not well aligned (centered).  If you are 1.5 to 2" away from the edge, you may be able to get away with your design not being perfectly placed.  However, when you are close to the edge, even 1/16" off will show.

Hope this helps!

Pat, The Avid Embroiderer