There is no logical reason to turn the Danes away. There are better reasons to allow them than to kill them or deny them entry:
1) They will provide additional labor for our people, whether as slaves or as assimilated Japanese citizens.
2) They might know something useful. What if one of those among the Danes, or one of their descendents is a great inventor (of Giant Death Robots), scientist, or achitect? Do we want our enemies to gain knowledge of this before us?
3) The people that join us may also be used as soldiers in the event of war with one of the surrounding nations.
4) Paranoid Xenophobes: Why should we worry about a tiny group of foreigners? We can seperate the children from the adults, let the adults die off, and then teach the children our ways. They will not contaminate our culture, and will provide additional labor for us.
@DT: EXACTLY!
And concerning stone: it is a production increasing natural resource that requires a quarry to access. It is like marble, except marble is a luxury resource that boosts wonder production.