I’ve worked with a lot of Wood PLA (almost exclusively Amolen). It stains fine, but I always apply a very small amount to a fine bristle brush and use that to apply it to the parts. I don’t use much, and then I let it air dry in a room that’s at least 70° overnight before doing anything else with it.
I don’t know that I’d ever sand blast. I’ve manually sanded (which has allowed me to better fake “grain” before applying stain.