The first thing that strikes my mind is (/proc/cpuinfo should be accessible from all snaps for reading):
cat /proc/cpuinfo |grep ^Hardware| sed 's/^.*: //'
... but i just noticed that the dragonboard CPU doesn't actually return a value for "Hardware:"
Alternatively perhaps shipping lshw in your snap and use the "hardware-observe" interface might also work.
And third, you could perhaps query snapd on localhost for the currently used model assertion somehow.