Back to spray cans, you can also get spray graphite lube (pretty sure that's aka "dry lube") and spray silicone lube.
Graphite is a fantastic lubricant, but being graphite it's 'dirty'. Probably not much of a problem in this case!
My first choice if grease is a no-go, is spray silicone, and I have a good reason:
About 3 years ago our now-19 year old but still like new Ridgeway grandfather clock started "hanging up", the chimes would run off slow, it would stop running after a couple of hours. I assumed years of dust had taken its toll. I tried gently blowing the movement out with compressed air, to no avail. Having used spray silicone a couple of times, I found it to evaporate nearly immediately, so I thought what the hey, and I just sprayed the entire movement's gear train and everything else in sight, rather liberally too- 30 seconds later there was no evidence I'd sprayed a thing inside the clock, and 3 years later its' still running perfectly--
If it won't hurt a $2500 grandfather clock movement, I doubt it'll do much harm to a motorhome slideout!
Walmart has it...