Hi Abe. Welcome to Permies!
Great questions about substrate products and I totally understand your situation where you are not able to chip up your own wood. I will try to answer your questions more directly and give you an option or two that might also work.
Firstly, I would think that the wood shavings would work. Do you know what species of wood these would come from? If you were getting something like aspen bedding litter (my daughter uses this for her rabbit), I would think you would be in very good shape. Pine shavings *Might* work, but generally conifers are to be avoided with Wine Caps. My understanding is that the sap inhibits the mycelial growth, but the pine shavings might be relatively free of pine sap. Honestly, I just don't know as I have never used pine and I don't know the actual condition of the shavings without actually looking at them. I would also avoid cedar chips. But if you can find just about any other non-conifer chip (again, aspen or poplar would be great here) I think you would be in great shape and these do come in big bundles that can be purchased at a farm supply store.
Secondly, I would suspect that Wine Caps would in fact grow on dyed bulk wood chips, I just don't know what is in that dye, what gets into the mushroom, nor if it is toxic to you if you want to eat them. Maybe you could find out what is in the actual dye. But I do know from experience that fungi will grow on that very type of wood mulch you are mentioning and if some types of mushrooms can grow there, then I think that Wine Caps would certainly grow there. My experience (which does not include pine or cedar) is that Wine Caps will ravage just about any type of wood!
So a couple of other options you might consider:
1) Can you get a good hardwood log and inoculate with pegs instead of sawdust spawn? This is the more traditional way to grow mushrooms--inoculating a log as opposed to inoculating chips. It might take a bit longer to colonize, but make no mistake, that log will get obliterated by the Wine Caps and the left overs will make great compost.
2) Another thought: Can you get straw bales? Wine Caps will grow VERY fast on straw bales--far faster than on my wood chip beds. I am tinkering with the idea of trying some straw bale experimentation this fall just to try out the idea. I did once have a straw bale that got accidentally inoculated from wood chips that had been inoculated with Wind Caps. The Mycelium had to expand about 4 feet to reach the straw bale, but in year one of accidental inoculation, the bale lost half its volume. But year two, the bale was reduced to being about 1-2 inches tall but still vaguely recognizable as where a bale had once been. After year 3 I could see no trace of the bale whatsoever. Straw bales yield up quick mushrooms but don't last terribly long.
3) The hybrid model. This is something like a Frankenstein
hugel bed. Maybe you could lay down some logs on the ground and lay straw bales on top. Possibly the bales would decompose very quickly giving you the mushrooms you want quickly, while the logs (oak is best, but just about any non-conifer will do. I use a LOT of Autumn Olive) would give you a longer supply and more compost.
These are just a few ideas and if they help, Great! If you still have questions, Fire Away!
In either case, once again, Welcome to Permies!
Eric