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Charles is available on iOS (and I think Android) and lets you intercept both Wi-Fi and cellular traffic without another machine required.

Yeah, seems like you should be able to use the headless mode + web ui to capture, then export for analysis.

Author here: it's totally doable. Please keep in mind that you won't be able to change settings values at runtime (e.g.: adding new rewrite rules). I tried changing the configuration file but the changes aren't propagated to Charles if it's running.

You can extend this over mobile network using VPN.

Device will use internet over VPN and on VPN server you will run Charles to catch everything.

You can definitely do this with fiddler. Very nice to use in conjunction with xip.io also