They can lift the prints, in theory, given that nothing happened to remove the prints from the item. Whether they do or not is another matter.
You could conceivably be charged under the theory of constructive possession. This allows multiple people to be charged with the possession of the same item. Its most common application is when there are several people in a car, and there are drugs in the car but no on any one person's body. Multiple people can be charged with possession.
This is a very simple explanation of a somewhat complicated area of law, but the example is good enough given the limitations of the information I have.
Please understand that answering this doesn’t create an attorney/client relationship between us, and as hard as I try to answer your question well, it isn’t legal advice. No matter how much information you put into a question, the answers you are going to get are still going to be vague. It is in your interest to contact a lawyer, most of whom will do a free consultation. Even 15 minutes with a lawyer is going to produce a more specific answer to your problem.
The government can charge a person with possession of paraphernalia based on either actual possession (if someone physically possesses the item) or constructive possession (if someone is "exercising dominion and control" over the item even though it's not found in their physical possession. The law on constructive possession is rather fact specific, so you'll need to talk to a lawyer who can get all the details from you in order to give you a better idea of the situation. For example, I'd want to know what the paraphernalia looks like, if it was possible for you to have touched it without knowing what it was, where exactly it was found, who else had items in the storage facility, etc. Good luck!
I might be more concerned about whether a credible individual would claim they saw you in possession of drup paraphanelia.
As far as fingerprint identification, law enforcement officers do not always lift fingerprints until a suspect has been identified.
If a fingerprint has been lifted, the Automated Fingerprint Identification System (AFIS) is often used to identify possible matches. If you are not in the AFIS system, then AFIS cannot identify you as a possible match.
If there is an AFIS match, or your fingerprint has been obtained in some other manner, then a fingerprint examiner looks for the requisite number of points of comparison to determine a match. The quality of the fingerprint and whether a partial print or a complete fingerprint has been obtained have a bearing on the number of points of comparison an examiner can detect.
I submit that fingerprint identification, unlike DNA identification, has not been subject to the scientific method and should not be admitted into evidence. In support of that argument, for example, I would point out that different jurisdictions and even different countries have different numbers of points of comparison to determine a match--while a scientifically reliable test would have a universal objective standard as opposed to a subjective standard. Fingerprint results, furthermore, do not have error rates or have been subject to peer review and mistakes have been made in cases involving fingerprint identification.