I'd say GREAT if you can work that out with your apartments but if you can't, just get a key from the customer. I've bid thousands of people for house cleaning. I'd go in, they wouldn't know me from Adam. Take me on a tour of their house..... now mind you I'm a male and most of the time the female would be the only person home while doing this..... I would present them with a bid sheet, they would choose which plan they wanted to go with..... Now they would give me a key to their house (sometimes worth $100,000 and sometimes worth several millions of dollars). They would ask me if I needed to be paid right then or should they leave it on the counter and if they had a security code they would give that to me. I'd know every little thing and all the secrets about their house and I've only met this person 10 minutes earlier. So I'm guessing that with you living in such a small complex, you could easily get the key from your neighbors.
My guess is that you are making a much bigger deal out of it than they will. Relax.... do you know what happens if you get 3 calls and none of them want to give you the key to their house? Nothing.... no one died. But really, giving someone a key to do a service is not a big deal. It's done millions of times in the US every day. You can go to the apartments if you want but personally, I'd just go directly to the customer.
Here is how I kept up with the keys we had. They were on a key chain that had a number on it (nothing else, just the customer number).... let's say 26. So now, in my computer I had the customer and the information and the key number.... 26. So even in order for us to know who the key belonged to, we had to get in to the computer. That way if you lose it, you don't have Cindy Maer 2601 S Main street Apartment 3 on the key chain. 110% safe.