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Basically as the title states.
I'm well aware that portable devices are very sensitive to movement, but does that mean it isn't really feasible to try record conversation whilst walking for instance, or is there anything that can be done to mitigate the interference from movement?
The Rycote portable recorder suspension will help a lot with reducing handling noise and also a good windscreen in essential. With these two things you shouldn't have any issues with getting very good recordings.
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But the cam grip won't isolate from hand and movement noise, the rycote will.
Wasn't that what you wanted?
I own a Sony PCM-D50 recorder and while handling noise can be a pain, there are ways to train yourself to avoid it. The Rycote will definitely provide relief, but so will training your hand to grip firmly in a comfortable position while managing the headphone cable. The cam grip will not provide the shock absorption needed to avoid handling noise.
If you recorder has a microphone input, consider getting an external mic: it might be cheaper than the rycote and sound better than the recorder's built-in mics.