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To signal one's allegiance to the Liberals as President, one could say to another player, "all my cards are Fascist and it matters not which one I discard! Tell me which card of the 3 to discard!"

Similarly, the Chancellor could hold out two cards to another play and say, "all my cards are Fascist; choose one to discard" and also pass the choice onto another player, again signaling trustworthiness.

Is this kind of move allowed (or should it be allowed)? Is it in any way "cheating?"

Yes it is cheating and called out in the rules.

Rules

Verbal and nonverbal communication between the
President and Chancellor is forbidden. The
President and Chancellor MAY NOT pick Policies
to play at random, shuffle the tiles before
discarding one, or do anything else clever to
avoid secretly and intentionally selecting a
Policy. Additionally, the President should hand
both Policies over at the same time, rather
than one at a time to gauge the Chancellor’s
reaction. Attempting to telegraph the contents
of your hand using randomness or any other
unusual selection procedure violates the spirit
of the game. Don’t do it.

Additionally

Discarded Policy tiles should never be revealed
to the group. Players must rely on the word of
the President and Chancellor, who are free to
lie.

Simply put once the election is over the President and Chancellor should stop all communication and move to quickly enact a new policy by following the rules and this should be done in a timely manner as to not give any hidden meanings from the actions.

• President draws 3 policies


• President discards one and hands the other two over at the same time to the Chancellor


• Chancellor discards one of the policies and then enacts the other one.


• At this point and only this point can the President and or Chancellor make claims about what policies they had to chose from

As a side note one very important thing to remember is that no matter what side someone is on they are going to make a claim about having no choice if a fascist policy is enacted. Also a claim can easily be made that the Chancellor was given a choice when a fascist policy was enacted and it was just a fascist President trying to make a liberal Chancellor look bad. The key point here is that the claims of what cards each player had to chose from need to be taken with a large grain of salt as you can easily lie about them.