transplant golden raspberry plants

I have a over abundance of golden raspberries in a location that I want to cover with concrete for shop floor

These are self volunteers, in that I have owned this property for over 40 yrs, I did not plant them, nor did my wife... There was an apple tree in this area, but it died and i cleaned up the trash, mowed the area and forgot the area... I put in a 40 ft steel storage unit, and over time had to add another building, spaced 12' away.... BETWEEN the two buildings is now full of green raspberry canes... The open area is sited north/south,  with wind protection east/west  

My question is, how can I move the existing canes, and the blooming / bearing canes are pretty, and tasty.... so I want to save... I also have two patches of "thornless blackberries" on the property, and they are about 100 ft away... These patches are several years old, both about 30' -to- 50' in diameter... They self water, rain mostly, with some irrigation thru landscape of yard when it rains ... As a side note, my wife and I do not believe in poisons / pesticides near our food we grow, nor do we use commercial fertilizer ... our go to is chips, leaves, manure, homemade compost with kitchen scraps, leaves, manure & chips ...

My location is Winston-Salem, NC

Can I just dig them up with a ball of earth, and transplant to new location

Yes, you can just dig up the canes and move as many as you feel like digging. Raspberries are tough and move pretty easily, in my experience. Just throw them some water on the regular, if it is dry, for the first year.
Last year, friends let me come out to their place and dig the yellow raspberries that were spreading out of their area and into an annual bed. I was not careful but just took everything that would be getting cut down and threw them in a big tote.
Then, I just dug enough of a hole to stuff each piece in, threw some mulch on them and mostly ignored them for the summer. ( I had a lot going on last year and that was all the effort I could give them)
A bit over half lived and are up this year.
I've now got them in the 3 areas I wanted and they are spreading out!

Yup, dig a big chunk of root and move them.

We have both golden raspberries and a vigorous red raspberry varietal that can't be beat. Dig up a big chunk and move it, stomp it in and give it a blast of compost and water -- and it will be unstoppable.

Yes.  should be easy as raspberry clumps typically transplant easily.  Usually need careful irrigation while reestablishing is the only problem typically.  If already growing well be sure you prune the tops back to match root damage.