In Shakespeare's Hamlet, Act Four Scene Seven; what does this scene reveal to us about Claudius' people skills and his man-management tactics?

Claudius is a brilliant tactician when it comes to getting
people to do what he wants without them even realizing that they are being manipulated. 
This is very evident in Act 4, Scene 7.  Earlier in the Act Laertes storms into the room
and demands vengence on Claudius and Hamlet for the death of the his father.  He is
angry that Claudius didn't do something to keep Hamlet in check, especially since he is
acting crazy.  He vows vengence at all costs.  It doesn't take but a short conversation
for Claudius to calm Laertes down and pin all the fault on Hamlet, and excusing his own
choices.  When Ophelia comes into the room and has clearly lost her mind, Laertes in
riled up again, but Claudius calms him down again.

At the
start of Scene 7 he tells Laertesto "put me in your heart for friend."  By strengthening
the closeness of the relationship, it makes Laertes more easy to control.  Claudius
comes up with a rational reason why they must proceed with caution against Hamlet
for the people of Denmark have "great love . . . [to] bear him, / Who, dipping all his
faults in their affection."  They are willing to forgive Hamlet anything because he is
so well liked, so they must proceed with caution.  After they learn that Hamlet has
returned to Denmark, Claudius asks Laertes "Will you be ruled by me?" and Laertes
responds that he will.  From then on, the game is on for Claudius.  All he has to do is
convince Laertes to kill Hamlet and all of Claudius's problems will be solved and none
of the responsibility will fall on him.  He convinces Laertes to challenge Hamlet to a
fencing match and convinces him with a long story that Hamlet is jealous of Laertes's
skill.  By appealing to his ego, he overcomes any qualms Laertesmay have had about
possibly losing to Hamlet.  Then, to ensure the revenge, they both agree to poison not
only the sword by a cup of wine.  If all goes to plan, Claudius will look completely
innocent of the death.  The final piece of his management of Laertes is his assertion
that they must act definitively because he understands that the things one want to do
need to be done quickly.  He says, we should do it
because

We
should do when we would; for this "would" changes,

and hath
abatement's and delays as many

As there are tongues, are
hand, are accidents.

Claudius
is echoing some of the same ideas that Hamlet talks about in the "To be or not to be"
soliloquy in regards to how thinking and the passage of time delay the momentum of
action.  Claudius doesn't want there to be any delay in their plans against Hamlet.  He
is the master of manipulation in his actions with Laertes and he is using Laertes to
achieve his ends.