I would have to agree with the others. Surgery is pretty tricky especially if the dog is on meds. Some medication is mood altering. If you could possibly wait at least a week to bring in the new dog that would be ideal. Males usually recover pretty quickly and are back to normal within a week. This will give your pooch some much needed rest & healing time.
To introduce the dog I would have them meet in neutral territory some sniffing & such & afterwards I would take a nice long long long walk around your neighborhood…like 2hours at least. Let them get used to being together with you on your walks. I would even make it a routine for a while until they get used to the pack order.
I would also suggest RULES from Day #1. Establish the rules of the house so both dogs understand that you're the boss & these are the rules...My rules I don't allow the dogs to hoover while I make their meals. They have to be sitting calmly until I'm done. They eat in separate crates & before I put their dish down they must sit & give me eye contact. I do the same for treats and toys...everything is given only if they sit calmly & give eye contact. There's no jumping on me EVER...if they do this they get my back which they hate because they love mom's attention 🙂
Good luck to you 🙂