Im a Super Clean Freak when it comes to My MLer's. I do a Complete Clean after I shoot it, even if it's just once and I mean everything that can be ytaken apart gets Cleaned. When I put it back togeather it looks's like Brand New.
Now of Course if I shoot it while Hunting I'll reload it and Not Clean it

but when I get it Home I tear it down.
My Wife Works Nights so If I Shoot a Deer I have something to do at night while She's Working, I actually Enjoy Cleaning My Mler's.
What You did should be Fine for time being, but since you use Pyrodox Pellets if your Trigger Mech can be removed and Cleaned as well as remving your Firing Pin I'd clean that too, you dont want your Firing Pin to Carbon Up and Not Fire if You Need it Too.
I Clean My Barrel with Dish Soap and Water with a Nylon Brush, followed by TC No13 Bore Cleaning Patches untill a clear patch, then dry patch it, followed by a wet patch of Montana Extreme Bore Conditioner, I let the MX BC set it the Barrel for awhile, then Dry patch it twice and she's ready for Loading. I wont get into all the rest of what I do to the rest of the MLer to clean it......
(BP)