109 Hey Dana ,
Defiantly 100% welfare of the animals first and foremost is the objective (so well done on reaching out), which in this case is protection of Jake, as you say will not defend himself against the aggression from Brody due to his differences.
Leadership exercises on your behalf found here https://www.dogtraining.world/start-self-help/leadership/ will definitely aid best practise to help both dogs in this regard (check it out for your information), defiantly take ownership of the situation (which you have done) in which both dogs are in the same presence of one another.
Is it worth the risk of not having Brody muzzled around Jake? IMO No defiantly not, I’d like to know the situations in which these aggressive instances are taking place, is this dominance aggression? is it resource guarding? is it territorial aggression? Then When and hows usually explain the whys….so to answer definitively your question ““will the muzzle cause Brody to become more aggressive or possibly less aggressive?” taking into account the breadth of information i would say will the muzzle prevent Brody inflicting injuries to Jake should they encounter one another in the future? YES ….and therefore protect Jake from the severity of these attacks?… YES.
Is that more important than possibly making Brody more aggressive at that moment…. ABSOLUTELY YES…
This will obviously lead into being more cost effective for you with regards to Vet care.
Its great that your looking to mitigate these outburst in the future, As you have said you are looking to keep them separated which is a great start.
Using a muzzle is not a bad thing, it is protecting the dog from injuring people, other dogs and themselves.
FYI Dana there has to be over 100 years worth of Handler/Trainer experience including all the trainee’s and trainers here at K9-1 plus a gold mine worth of info found in the knowledge base section as well as the forums of past and present so stay positive, and keep us posted.