I see 3 possibilities.
1) probably best one but requires mesh design : include the shaders/effects in your unique weapon mesh. I have no experience in that but it is possible as shown in the mod "Burning Weapons" (unique dremora weapons with flame effect coming from animated fires. Great visuals compared to particle shader, but requires a special mesh and so useful only for custom weapons, and active at all times.)
2) Using one of the non-used Magic Effects in the CS and make them use a specific shader you create. This is easier but the major drawback is that non-used magic effects are not many and could be used by other mods, creating conflicts. So this is more or less dangerous is you plan to distribute your mod, for example.
3) Using the "Script Effect" magic effect for your weapon. Now customize the enchantment for your weapon to call a script you make, and in this script maybe you can try to use the function : setMagicEffectEnchantShader to change the shader when you equip your weapon. This road can be investigated, but as always beware of side effects as you're modifying the "Script Effect" magic effect that is used by the game and many mods. That' why setting it back to "no shader" if you unequip the weapon looks necessary to avoid having the shader popup on other objects using scripted effects if you didn't set it back to the original null value.