There’s no need to mention your agent to the publishers if you’re the one doing the researching and submitting. Just have a conversation with your agent about the situation before you proceed. That’s necessary for your professional relationship—and you may need to put something in writing to address language about “next published work” in your agency contract. If the agent still wants to be part of this gig, then work out an agreement for this one book where you do the legwork and the agent makes the contact and negotiates the contract for a smaller percentage of your royalty. I’ve personally seen that scenario, with all parties happy about it. It’s professional and fair to all.