Yes it can be shipped UPS but there are a few simple rules.
https://www.ups.com/us/en/help-center/packaging-and-supplies/special-care-shipments/hazardous-materials/shipping-ammunition.page
Be sure to put an ORM-D sticker on the box and you will probably have to take it to a UPS hub/freight center not a UPS store. You can find the UPS hub nearest you by using...
https://www.ups.com/dropoff - click 'see all options' then, check 'world wide freight centers', then 'search'.