Do you need a strap at all?
I just glued (With Uhu glue) some of that anti-slip rubbery matting stuff to the underside of my ordinary A4 clipboard, my pen clips (using its own clip) on the bit that sticks out for the clipboard used for hanging it up.
The non-slip bit, available from the
RNIB (for example) or on good sized rolls from the likes of Woolworths, and if you have them in your neck of the woods Wilkinsons.
The clipboard doesn't shift for me during normal or utility manoevers (not tried it for spins though).
My stop watch I attach to the clip bit of the clipboard with a loop of elastic material.