For the AP61100, you can look in the datasheet:
https://www.diodes.com/assets/Datasheets/AP61100-AP61102.pdfIt should work fine at close to 100% duty cycle though.
For example, see page 14 where it explains how you can determine the Ton period which like Toff must be minimum 70ns :
The AP61100/AP61102 device is a 2.3V-to-5.5V input, 1A output, fully integrated synchronous buck converter. Refer to the block diagram in
Figure 5. The device employs constant on-time control to provide fast transient response and easy loop stabilization. At the beginning of each
cycle, the one-shot pulse turns on the high-side power MOSFET, Q1, for a fixed on-time, tON. This one-shot on-pulse timing is calculated by the
converter’s input voltage and output voltage to maintain a pseudo-fixed frequency over the input voltage range.
Ton = Vout / ( Vin x Fsw)
where
VIN is the input voltage
VOUT is the output voltage
fSW is the switching frequency
The off-time duration is tOFF and starts after the on-time expires. The off-time expires when the feedback voltage decreases below the reference voltage, which then triggers the on-time duration to start again. The minimum off-time is 70ns typical.
See Figure 15 on page 8 for switching frequency vs load - in your case at around 0.1A you're looking at around 500 kHz switching frequency.
So for example let's say 3.1v in, 3.0v out, 500 khz switching frequency ...
Ton = 3 / 3.1 x 500,000 = 1.935e-6 or 1935 nanoseconds
Page 19 has example of pcb layout - it's only missing the connection to enable pin, which could be permanently connected to Vin
As for the second regulator I suggested, the datasheet says it can do 100% duty cycle, so no worries.