I was wondering if Schottky diodes would be the best option because of
there low forward voltage drop?
Probably. A typical 6V dry cell battery has useful capacity down to ~4V (1V per cell) and your telephones are probably designed to work down to this voltage only (if they could use a lower voltage then why have 4 cells?).
A silicon bridge rectifier drops ~1.4V (about the same as having one flat cell) which may significantly reduce the operating time. A Schottky bridge drops ~0.8V.
Here's an example 6V AA discharge graph. I have copied the original curve to show what you would get with 0.8V and 1.4V drop through the rectifier. In this example (80mA average current draw) the ~12 hours run time is reduced to ~7.5 hours with a Schottky bridge and 2 hours with a silicon bridge.
In practice it might not be quite this bad because the current draw will probably be less at lower voltage, but you get the idea.
I don’t know if the higher reverse leakage of a schottky would be
detrimental to proper function.
High leakage is generally only a problem if the diode is rated for much higher current than needed or is being operated at high temperature. Leakage current also increases as voltage approaches the diode's rating, so choose a rectifier that has much higher voltage rating than needed but not much higher current, eg. 1A 30V rather than 3A 10V.
Finally, consider the current draw of your phones. If it is much higher than the leakage current (likely) then it shouldn't be a problem. A higher current diode may have lower voltage drop which is more important.