Mythras treats a weapon's damage-reducing abilities when used to parry or block, separately from the weapon's own resistance to damage. It also bases damage-reducing abilities on the relative sizes of the attacking and parrying weapons. This means that a character armed with a dagger (size Small) just isn't going to inflict any damage at all on someone parrying with a kite shield (size Huge), but would inflict some damage on an opponent parrying with a shortsword (size Medium).
The default position Mythras adopts is that, in general use, weapons don't break as frequently as they might in say older iterations of RQ, and for that reason doesn't have rules for weapon attrition when used for parrying successful blows. Of course in reality, bronze blades are more brittle than iron ones, and iron more brittle than steel - but we decided to forgo such fine distinctions in favour of a simpler approach where all metal weapons are treated in much the same way. It is a compromise, but it also simplifies book-keeping because one doesn't need to worry about how many Hit Points your weapons lose when used to do something they're designed to do, in the hands of people trained to use them (which is another important factor in weapon breakage).
However, it is possible to target a weapon directly, making it, rather than the wielder, the focus of an attack, and so Mythras has rules for this under its Sunder mechanic. Some weapons have Sunder as an available Special Effect, and these tend to be weapons designed for inflicting lots of damage (a greataxe, say) and/or being equipped with specialised surfaces (such as the spike of certain polearms) to puncture armour and shields. Damaging weapons in Mythras is therefore a deliberate, rather than an incidental act, but there are certainly rules for it. Sunder is very useful if an attacking character is being kept at range by an opponent within a longer weapon (a spear or pike, for instance). It may be an effective tactic to attack the weapon and damage it beyond use, allowing the attacker to then close with the (now disarmed) opponent.
For Lloyd's situation, where shields or other protection degrade when absorbing or ablating damage, it would be quite simple to give certain weapons the Sunder trait, meaning that whenever a shield is used to defend against them, their Hit Point value reduces if the shield's Armour Points are overcome. It's really all about defining what certain weapons can do when coming up against certain defensive types. Lloyd likes this fine level of detail, so assuming the additional book-keeping isn't an issue, then using the Mythras Sunder mechanics might be a solution to consider.