Remus Lupin to Harry in Harry Potter and the Prisoner of Azkaban Chapter 12, Page 237 (US Hardcover First Edition)
A Patronus is a kind of positive force, a projection of the very things that the dementor feeds upon - hope, happiness, the desire to survive...
Nowhere in canon is there any indication of a Patronus being a physical being, other than when Harry's Patronus uses its horns against a Dementor. (Expanded upon later in the answer) Otherwise, they appear to be made of light, and not of real substance, even the corporeal ones.
Intentionally being vague so as not to introduce spoilers:
They have the ability to project their caster's voice, as shown in an earlier chapter of the Deathly Hallows. They have the power to fend off Dementors, and Snape was certainly able to use his to guide Harry, but none of this indicates enough substance to interact with everyday objects.
Using the movies as canon, we can see that the waves of light emitted by Harry had an effect on the dementors, and not on the trees around them, which indicates that the ability to physically push back dementors is limited specifically to dementors. They can throw a dementor, but not so much as stir a leaf on a tree.
Using the books as canon, Kingsley's patronus passed through the roof of the tent to deliver its message, further indicating that they lack physical substance.
If this is the case, then a Patronus would have no way to pick up a physical sword.