Your website indicates most varieties of English hawthorn are thorny, but implies there are some that are not.
We don't recommend vendors but you can inquire at your local nurseries or do an online search for reputable nurseries that ship.
https://www.gardeningknowhow.com/ornamental/trees/hawthorn/thornless-cockspur-hawthorns.htm
two years ago they were full of berries - lat year nothing. I don't remember if they bloomed. Already this year they have leaves but have not bloomed yet.
They should be starting to bloom very soon! Usually, it is April through June for most varieties. Some flower first, and some flower and leaf out at the same time.
Trees are often grafted onto a hardier rootstalk to improve the winter hardiness of a plant, for one reason. Rootstalks in themselves are not usually a tree you would want. That's why it's important to remove suckers, so they don't take over the desirable top of the tree.
Hawthornes are often used as a rootstalk for fruit trees. Here is an article you might enjoy:
https://www.gardeningknowhow.com/ornamental/trees/hawthorn/grafting-a-mayhaw-tree.htm
https://www.gardeningknowhow.com/ornamental/trees/hawthorn/thornless-cockspur-hawthorns.htm