I had the discussion about the very same setup of mechanical bridges with the EPBF ref about 2 years back and the call would be foul in this case as the equipment was not intented to be used this way. Even without the chalk it would be foul. WPA rules are clear on this:
1.3 Player’s Use of Equipment
The equipment must meet existing WPA equipment specifications. In general, players are not
permitted to introduce novel equipment into the game. The following uses, among others, are
considered normal. If the player is uncertain about a particular use of equipment, he should
discuss it with the tournament management prior to the start of play. The equipment must be
used only for the purpose or in the manner that the equipment was intended.
(See_6.15_Unsportsmanlike_Conduct 6.17 Unsportsmanlike Conduct.)
(a) Cue Stick – The player is permitted to switch between cue sticks during the match, such as
break, jump and normal cues. He may use either a built-in extender or an add-on extender to
increase the length of the stick.
(b) Chalk – The player may apply chalk to his tip to prevent miscues, and may use his own
chalk, provided its color is compatible with the cloth.
(c) Mechanical Bridges – The player may use up to two mechanical bridges to support the cue
stick during the shot. The configuration of the bridges is up to the player. He may use his own
bridge if it is similar to standard bridges.
(d) Gloves – The player may use gloves to improve the grip and/or bridge hand function.
(e) Powder – A player is allowed to use powder in a reasonable amount as determined by the
referee.
You can use two mechanical bridges to support ONLY the cue, to use the bridges to support your hand is not allowed as it is not on the list of allowed use of equipment.