If you have sick time/CTO time at work and won't get in trouble for using it: use it! (Even if for a day or so - if you go three they'll probably require a doctor's note, so don't over-milk it.) My suggestion would be to say that you've apparently caught a mysterious gastrointestinal bug (very Nurgley!) and are sluicing out both ends. That's sufficiently descriptive that nobody will likely question further, everybody knows exactly what you mean, you're not physically injured but sufficiently incapacitated and contagious enough that nobody will want you around them, especially if you say you have to keep running to the bathroom every 10 minutes. And likewise just as mysteriously: it completely disappears in 24-48 hrs. with no lasting effects. (Day #3: you call work before your shift and say you're feeling overall better, but you're going to the doctor's to get checked out and the earliest appointment they have is late morning/early afternoon. You paint. You go to the doctor's office and tell them your "symptoms" the past few days but that you seem to be feeling better. You (unfortunately) pay for the office visit, but at least you'll officially have a clean bill of health you can take into work later that day.)
Day #1: You call in before the scheduled start of your shift (perhaps AS you're painting) and say you need to get a jumpstart for your car because it apparently won't start and it seems like it's the battery. You're just waiting for your friend/housemate/relative/significant other and will come in as soon as you can. You paint for a while, and then go in 1-2 hours late, saying it started okay and seems to be in working order.
Day #2: You call in before the start of your shift again, sounding aggravated. Your f'ing car won't f'ing start again, and it's doing the same thing it was yesterday - seems to be the battery. You're just waiting for your friend/housemate/relative/significant other left early this morning/today to go shopping and so you have to wait for the towing service to come give you a jump start. You paint for a while, and then go in 1-2 hours late, saying it started okay after the tow truck showed up and seems to be in working order, but you're going to get it checked out tomorrow/the weekend.
Day #3 (potentially): If you have sick time/CTO time at work and won't get in trouble for using it, then you call in before the start of your shift and are taking the car in to get checked out before you come in. You call 1-2 hours later and say you're at the auto shop getting your car checked out, and the place is pretty busy. You call back 1 hour later or so and say that they checked out the car and it doesn't seem to be anything major - they're suggesting you get a new battery, so you did, and you're on your way into work. (Now if you call in before your shift and they'll ask for proof that you took your car in, then you paint for an hour or two and then take your car in to an auto shop - you explain the "not starting & needing a jumpstart problem" and that you want to get your car checked out. You call work and say you're at the auto shop getting your car checked out, and the place is pretty busy. Your car gets checked out, and you (unfortunately) pay the not-so-serious diagnostic fee and likely there's no problems to be found - and if they suggest you get a new battery, you tell them it's money you don't really have to spare right now and if it acts up again, you'll come in and get a new battery.
(If you don't have time off, tell work you'll take the car in at the weekend and you say the following week that they either couldn't find anything wrong or you had to get a new battery.)
I wouldn't tell work that anyone has died or is sick as that's just bad karma (even if it is rather Nurgley).
The other thing to keep in mind is that GW is not a machine, nor a hospital, nor a psychiatric facility, nor a court - it's a hobby-oriented company made up of people that are by and large people-oriented and generally personable. You paint/rust all of the important figures so you've got an army to take for public display, and if there's a few left over needing to be finished, then you tell them that (because unlike for them, your hobby is just a hobby, whereas for them, your hobby IS their job) and just bring in the finished figures in a day or three after the rest - I'm sure they'll be understanding. Realistically, Pandemic is going to be sitting in a display case for at least a month or so and a few figures, maybe one per squad, added a day or three after the fact is by no means a dealbreaker. Worst case scenario: you paint the last-minute ones as well as you can overall and only weather them from the waist up, and then proceed to hide them at the back (or middle, depending) of their respective groupings... then when you have more time, you sit your butt down at Warhammer World and finish up the last remaining guys completely where they go back to sitting in their cabinet on display for people to "ooh" and "aah" over.