Some general comments.
The round has to be subsonic. you can't silence a supersonic shock wave. You can alter it with echos (sonicator), but not "silence it".
The .22 LR is a popular assassin round. However...you can only use stock ammo. You can't custom load a .22 round. (It's a rimfire and liable to go off in the loading process.) There are weaker, and more silent version of a .22, all the way down to a .22 CB cap. (Which is just the primer charge and a BB). Note: the lesser rounds won't work the action, too little pressure, unless the gun is custom modified for the lower pressures. (One reason why .22 revolvers are still used...)
.25 ACP is very similar to .22 LR from a ballistic standpoint, and being a centerfire, it can be custom loaded. It is used in autopistols only, and usually very small ones. (Beretta is the common example), They are ofter referred to as "ladies guns" or "garter guns". They can be modified for "silencers". Strictly designed for close range work. This seems to be a perfect fit for your character.
As to the toilet paper "silencer", it might catch fire from the unburnt (but still burning) powder. and at the range described, traceable powder will be found on the shooter face, as well as hands...
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