I'd be really happy with Dudley or Shanahan. Yes, everyone on the list of potential "advisors" has flaws, as does the idea of an "advisor to the GM" instead of a POHO. However, there are benefits.
By a lot of accounts, Buffalo is considered a nice place to live by many in the hockey world. The Sabres have long had a reputation for taking care of players, from a very giving owner to a GM who trades players at the deadline to go win Cups. There are very few comments to the contrary.
Where Buffalo has a bad reputation is management decisions. They just can't win. Make a batch of cookies and pour in some vinegar. It doesn't matter about anything else, the cookies are bad now.
I think Buffalo has drafted well, and do a decent job of development in Rochester. I also think they make some good trades. But no one wants to come to Buffalo as a free agent or drop their NTC/NMC for Buffalo. Imagine if it were different. Matt Murray accepts a trade to Buffalo, and the Sabres come out of the draft with Marco Kasper, Ostlund or Savoie, and Kulich. Things like that are happening all the time, based on Adams' reactions at trade deadlines and in the off-season.
Imagine you're Sam Bennett. You're literally exactly what Buffalo needs to win. Adams calls your agent, and you're offered the best contract you're going to get by $1-2M. But you're not interested in Buffalo, so you move on. So you tell your agent to turn Adams down. That's right now.
Now imagine that same scenario, but then your agent says Shanahan or Dudley want to talk to you. You're taking that call. You'll listen, at least.
I'm not saying either of those two guys changes anything. Not saying people start signing in Buffalo or dropping their NMC/NTC. But at a minimum, they'd give the organization a shred of legitimacy which they currently do not have.