For the price of a mosfet and a diode I don’t think it is worth risking.
Talking about "risking", you make it sound easier than it is. But do this properly. Wrong dimensioning of the power path switch components against capacitive loads may cause a catastrophic overcharge situation. Been there, done that, followed appnote, FET blows short in certain conditions applying external power supply directly to the battery, had to recall. It's not nice.
It's one thing if your product fails by
stopping working after an input voltage surge incident. It's another thing if it fails in a way of connecting the input directly to the li-ion cell, unprotected, from that moment on, while the product still appears working. With a 5V supply and one diode drop (assuming the diode didn't blow), it will be funny how it charges the cell to around 4.5V and everything kinda seems working....
There is no easy way out. Do a proper design with full analysis. Allocate a lot of time for this, especially if you are not experienced.
I hate many of these "looks nice&easy" li-ion products because you
think they give you an easy way out of lithium ion safety issues, but when you start designing one in, suddenly you find that the IC does not integrate the functionality you needed (and what the product exists for), and you find yourself following an appnote written by an intern which requires putting in a large number of external discrete semiconductors, high-value capacitors, often large-value ceramic with no snubbing directly in the input, etc. These are recipes for disaster.
Most li-ion ICs are not providing any safety, have no safety approvals, and you as the designer need to understand every internal detail about them. It sucks, yeah.
In general, power path switching kind of sucks, more or less. Especially if the load current is small as is the case here, I would be very tempted to connect it "directly" to the cell, and find a charger IC that doesn't go haywire. If they do, they sound unreliable in any case.
The issue is, the controller FET (linear or switcher)
is controlled with an actual current limit (and/or some kind of SOA protection); the power path switch FET which connects the input to the load directly
should be the same, but for some strange reason, following the appnote examples, they always slap bare unprotected MOSFETs to switch the load, with no protections whatsoever. This is a recipe for a disaster once you understand what they are actually suggesting you to do! Outside of such use case, you would never do that, but use a protected IC load switch instead.
So, my bet is, use one specified to be operated with a directly connected load. You sidestep the whole power path switching issue, and only have one protected path (the regulator itself) from the supply to the battery.
Do note, they have even a paragraph of "Selecting The MOSFET" which fails to mention any of the required parameters, instead bullshitting about "gate threshold voltage", showing the poor guy who wrote it has never properly chosen a MOSFET for switching in their life.