Neither are grammatically correct. Colloquially, you can get away with "there's nowhere to get hold of" and people will understand what you mean. The second phrase should be "There's nowhere to put my hands" or you can say "there isn't anywhere to put my hands." The words here, there, somewhere, nowhere, and anywhere all indicate location already. Words like "on" also indicate location. You only need one- thus when you say something like "I need somewhere to put my hands on" the "on" is redundant.

To have a semantically precise answer, the best choice would be, "There's nowhere to get a good hold." This is because there is certainly a place to put your hands, and also a place to hold the box, for example the bottom, but these might not suffice for easy transport or lifting. You want a "good hold" for lifting and transport.