While I'm being anal-retentive:
F/SN is really vague about this because all of the magical lore is explicated by characters with various misconceptions about what they're doing, but projection is at least theoretically capable of producing permanent "real" objects (as observed with Shirou's completely persistent conjurations, and the fact that he had to be told that objects created via gradation air were supposed to dissipate).
However, I think it's an open question as to whether Shirou's projection magic is merely a hyperspecialized extension of ordinary projection, in the same way that all Mysteries can be explored in depth, or if Shirou's applications of Projection are completely unique to him on account of his Element and associated Reality Marble.
In the former case, sufficiently advanced visualization techniques and spellcasting methods (realized in Shirou's case through the aid of his RM, and in Joe's case by the fact that he's not baseline human) are probably sufficient to advance projection magic to that new plateau of creating permanent projections, falsifying histories, etc. In the latter case, Joe is completely out of luck on account of his not having Unlimited Blade Works, though he might be able to do some novel research work and fill in the blanks by using his demigod nature and descent from Hephaestus or somesuch.
Either way, though, projection magecraft is fundamentally about falsifying objects which "already exist" in some sense; the transient replication of existing objects not at hand is given as the primary (only) use case for ordinary projection, and Shirou himself is seemingly unable to visualize and project novel creations, even with access to an arbitrary amount of blueprints to recombine or crib from.
So I think that it might fit for Joe to be able to copy effects like Master Craftsman and the Secret of Steel, but only when replicating items to which those effects had already been applied normally. He could project a copy of a sword forged with the Secret of Steel, but not project such a sword from scratch.
But that's just, like, my opinion, man.