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You should be fine, just be careful stripping the area you want to solder. The wire is still metal, it'll probably just heat up faster since it's thinner.
You could also cut the wire, and crimp connections onto the end. Soldering is definitely the more secure way to go, as the crimped connections have a way of falling off after a while, but either way will work.
If you're worried about damaging the wire, then cut open a spot far enough from the connector that you could still crimp a connector on there if you had to. That way, if you can't solder it, you still have the option of putting connectors on there.
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