I guess it's not actual, but can be useful for someone later on.
Weapon skill is a characteristic, so we use the rules under characteristic bonuses, what says:
" In addition to its numerical value, each characteristic has a
characteristic bonus, a number equal to the “tens” digit of that
characteristic. For example, a character with a Strength of 42
would have a Strength bonus of 4."
-DH 2E Core rulebook pg. 21. topright corner
When you get a bonus for aim, or lightning attack, you get that bonus for that test. So your characteristic stays the same as well as your characteristic bonus.
In your example, the character would cap at 4 attack.
Another example is wearing armour. If a character wears a Chainmail Suit, it caps their agility at 35. So if the character would have 40 agility so a 4 Agility Bonus without the Chainmail Suit, his/her agility and agility bonus would be 35 and 3 respectively wearing the armour. This is because the modification applies to the characteristic, and not the test made using the characteristic. Wearing the Chainmail Suit, a Routine(+20) agility test would succeed on a roll of 55 or lower, but the character's agility bonus still would be 3.