I offer my guests a shower after our time together. Don't ever be in too much of a hurry that you miss something, like perfume or hair.
I know there are plenty of reasons/excuses my friends have given, so I hope you get a few good ones. The gym always works, unless you have a bad back.

Another tip I can suggest. Choose providers that are low volume. They are usually well established, have comfortable incalls and will offer you the time and facilities to freshen-up before you head home.

xoxo

Sexy Carolina

Take a shower before you leave if you are going to be arriving back at home and your spouse will be there.  Another option is to join a gym as you can clean up there as well.

Running into someone you know in an apartment complex? I'd say you would be pretty much screwed...

I hobby pretty close to home but I'm aware of a couple of providers who are so close as to present unnecessay risk.  (Incall next to neighborhood highway entrance, where my car could be ID'd).
I aways buy gas, snacks locally.  If I had to buy outside my normal traffic area, I'd be forced to pay cash.
EZ pass tolls would confirm you were somewhere you should not have been but if someone goes that far to check you, you've already raised suspicion.  Still, I'd not want to provide evidence to confirm the suspicion.

I'm afraid I have no answer to being identified at an appartment complex or even a hotel...  where you have no legit business.  
skb

Here's a few things that come to mind-

If you are REALLY worried- come to the incall, have a light hug and kiss, and then IMMEDIATELY hang your cloths up or fold them neatly before more action ensues...!! This elminates worries about stray hairs, tolietry smells, smugged make-up... and even MORE damning- suspicious large pre-cum stains on your boxer shorts!!

I agree with others that saying you are going out running or went to the gym is excellent.  The gym explains why you are arriving home freshly showered and possibly in different cloths. It also means that you will bring your own body wash in the gym bag and not leave smelling like the flowery wash the lady might use. Alternatively, saying you were out RUNNING explains why you would arrive home sweaty and rumpled and want to head immediatly to the shower at home! ie "Honey, I would love to give you a hug... but I'm all sweaty and stinky- let me take a quick shower first.. (At which point you wash away any "evidence." )

As far as running into people- have a tentative back story in mind of why you are supposedly there... Also- consider employing the wonderful world of sun glasses, baseball caps etc... These articles are not JUST for celebrities! They help the REST of us remain incognito as well.

My .2 cents.

Several good answers to question #1.  I always shower after an incall appointment if I'm going home.  Yes, I take in my body wash from my gym bag (always kept in the car) for the same scent.

#2--If recognized try this:  "Hey Dude, nice to see you.  Oh, I'm here to pick up a work coleague, we are going to the game, driving range, bowling ally,etc."  If you are any kind of handy man, I'm here to help a work coleague fix his/her ______."

Be safe all.

At least wash your face after so the fragrence dur pussy isn't there to greet her when you walk in the door.  
Most professional ladies are smart enough to not use noticeable fragrences without checking with a gent...  usually on extended dates.  Yes, that would be suspicious!  
skb