Can I do a visa run for a Non-B visa in Penang without canceling my work permit?

While you could exit the country without canceling your current extension and get another Non-B visa to change jobs, when you go to get an extension on that visa they will see you didn't cancel your previous extension the official way and fine you for overstay 500baht a day for every day that went by where you didn't cancel your old extension (with a max fine of 20K baht).

You NEED to do both the work permit and the extension the correct way or you will have problems down the road especially if you are ever going to work here again

You do not have a Visa, but an Extension of Stay based on Working. On the day you stop working this Extension of Stay becomes invalid. But you have to go and cancel it, to get some time you can do it 1,3,,5 or even a week before you stop working.

If you wait till the last day of working you have to leave immediately, if you do it 1 day before 1 day, 2 days before 2 days etc.

I guess than if you look in your passport you see a big stamp with the second line: Extension of Stay is permitted up to 31 July 2018. If correct than you also have to cancel this Extension of Stay at Immigration before you leave the country, you can do this in advance to have some time to make travel plans. You need for this the cancellation papers of the work permit but also those you can get in advance.

You have to cancel this Work Permit and your new employer applies for a new work permit. Are you on a Visa or on an Extension of Stay and doing every 90 days reports at Immigration?