Connectors with 14 or 16 pins and D+/D- are commonly available from major brands/distributors now. Digikey list these under 'Number of contacts: 24 (14+10 Dummy)'. This
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I've used the Molex 2171790001, but many are similar. The smallest pads are generally 0.5mm pitch, so no worse than a fine pitch QFP in terms of soldering.
CCx are Configuration Channel pins, they have no bearing on the data connection.
They do if your device will connect to a dual-role port, in which case the CC pins with 5k1 pulldowns allow the DRP to detect a device connection before enabling VBus.