Sounds like your are in the same boat I was in a little while ago with my RCR2/15270 3 volt batteries.
So I decided to do some battery research. It turns out that all 3 volt rechargable batteries are Li-Ion unless it says that it is a LiFePO4 battery. LiFePO4 batterys are made with a different chemistry and must be charged on chargers that are made for LiFePO4 batteries because they are true 3 volt cells with a maximum charge of 3.6 volts. While, Li-Ion batteries which are usually a LiCoO2 have a normal voltage of 3.7 volts and a maximum of 4.2 volts.
**battery terminology - Primary battery means that it is nonrechargable [an alkaline AA battery is a primary battery] and secondary battery means that it is rechargable [NiMH, NiCd, Lead acid, Li-ion are all seconday batteries].**
Li-Ion manufacturers wanted to sell a secondary battery that could be used instead of lithium primary batteries like the CR2 or the CR123 that you find in stores. The Lithium primary batteries are made of LiMnO2 and cannot be recharged and have a normal operating voltage of 3.0 volts. So manufacturers use a trick of electronics to make a 3.7 volt Li-Ion cell work at 3.0 volt by putting a diode with a specific voltage drop of 0.7 volts in series with the battery. What that means that the diode uses up 0.7 volts of the battery which means 3.7 volts minus 0.7 volts equals 3.0 volts.
So unless you bought some LiFePO4, the AG-126 or the TR-001 are perfectly fine chargers to use to recharge your RCR123a/16340 3 volt batteries. So long that they are protected. I wouldn't suggest using any unprotected Li-Ion battery, because I just don't like the possibility of an exploding battery (mainly in the face).
Fun Fact
Actually those chargers can only charge those batteries to 90%-95% full charge bacause along with the 0.7 volt diode they have to put another diode facing the other way so that the battery can be recharged.(Diodes act like a one way street for eletricity) All Diodes have a voltage drop and the recharging diode has a lower voltage drop closer to 0.2 volts. So the Li-Ion cell can only be charged to 4.0 volts. You wont find any chargers designed specifically for RCR123a Li-Ion 3 volt batteries because a regular Li-Ion chargers works perfically fine.