I checked the game code. I can't interpret all of it, so here's the code of part of the Handiness Skill:
<UpgradeChanceFailMax value="25">
<!--The chance of failing an upgrade at the initial level when it can be done (the level of upgrade complexity). Chance from 0 to 100-->
</UpgradeChanceFailMax>
Since EA provides handy comments in most of their code, I can guess that there is a 25% rate of failure if your Sim is only
just at the required level of Handiness to upgrade an item. Pairing it with the Guide, here is a comparison:
If Bob Sim is upgrading a Television to have more channels (this upgrade requires Level 7 Handiness) and he only has Level 7 of Handiness, there is a 25% chance of him being electrocuted and singed. If he does it again, while still singed, there is a 25% chance that he will get electrocuted, this time, fatally.
So back to the Original Question - your Sim has a greater chance of being electrocuted if he has only just learnt the upgrade. Since you said that he has Level 6 Handness, if he does something that requires a lower level (Like make the Dishwasher run silently, which requires Level 3), he will have a lesser risk of being electrocuted than if he did something that required Level 6 Handiness - like Improved Crushing upgrade on the Trash Compactor.
Of course, all of this is moot if your Sim is upgrading a Plumbing Object, like a Sink.
Someone please correct me if this is wrong.