I gave my husband a bike as a surprise. He was not expecting it and was not involved in the decision-making. I knew what frame material and builder he liked, otherwise, I picked everything. This worked well because I knew what he liked better than he did (I just know bikes and the bicycle industry better than he does). He loved that the bike was a surprise.

When he decided to gift me a new bike, it was not a surprise. He gave me a budget and told me to pick out whatever I wanted. I would have HATED it if he picked the bike himself!

As you can see, people are different in this respect. Only the OP knows his wife and whether she would be happy with a surprise bike or would want to be involved in selecting frame/components.