I would rewrite it as a simpler sentence:
Once Tom had received Harriet's letter, he had an offer that he could either accept or reject.
It's not usual to add "in his hands" to "receive".
As to the difference between "It is in your hands" and "It is on your hands", it does depend on the context in which they are used. Both could be a simple physical description, or could be indicating resonsibility for action.
Student or Learner