Nine times out of ten, a classic engine is worth more complete as a near-running piece than to part it out. I've sold engines before. One of them was a 1966 Chevrolet 396 350HP factory engine. It had never been rebuilt. The client and I discussed and researched what it was worth all together (matching head and block numbers, original pistons, etc), and the overwhelming evidence showed that the engine was worth $1,000-$1,200 in my area complete. I sold it for $1,000. Had I parted it out, it would have netted $800. The matching numbers and all the fact that it was all original helped boost the price.
I have no doubt that a lot of the parts on this B&S fit other engines from the same time period. But if you don't know which models they fit, then how can you advertise as such? If you do know, then go for it. But there is something to be said for selling it all at once as opposed to waiting possibly months before it's gone from your garage.
And with the original owner's manual, I wouldn't even bother parting it out. Having it as complete as it is, with the literature, will help boost it's value to collectors and enthusiasts.