If this is a troll post...
I have a Mosquito, and I have a YHM Phantom. Looking at the two of them it has never occurred to me to try and combine them... It would be so heavy and large it would just be ridiculous. You can get adaptors for anything, but that don't make it right. And yes, I'm sure the YHM 556 would fully obstruct the sights on the Mosquito.
I think most people will tell you that shooting .22lr through a sealed can like a 556 is kind of a no-no. You will eventually fill up the can with built-up lead deposits, decreasing its internal volume and effectiveness. The other risk is that when firing 556 rounds through it, you can shake/knock loose some of those deposits. If the bullet contacts any of those deposits before it leaves the can, its trajectory can be altered with potentially fatal consequences, like if the bullet gets diverted through the endcap or baffles.
I think you should invest in a nice little .22 can. I use my .22 cans more than any others, they are well worth the money you'll spend on them.