On the face of things, you are either paranoid, or doomed. If "they" are after you (by "they" I mean the whole apparatus of political police that they have in China), then they will try to track you down and they have several ways for that, because they are powerful and determinate, and computers tend to leave traces of their action everywhere.
Your model is not fully defined, because you do not tell where you physically are at the time you want to do the uploading. If you are in China at that time, then know that public WiFi hotspots are actively monitored. Connections to a well-known Europe-based dissident FTP site are likely to trigger alarms. Even if you go through an anonymizing service like Tor, then you are not out of reach:
Video files are big and have distinct sizes. Data size tends to leak after encryption (encrypted data size will match cleartext size within a few bytes). If a video file of size 23.454739 MB appears on a dissident size, then Chinese police just has to look in their logs which public WiFi was involved in uploading a file of that size in the previous days.
Tor works by using a number of collaborating "relays". The Tor user chooses (randomly) a sequence of relays, from an "entry point" to an "exit point". The exit point sees the data, the entry point sees the source IP address. If China forces are at least half competent, then they already operate several (many) Tor relays. If, out of bad luck, you randomly choose as entry point and exit point two such relays, then they will correlate traffic (by size and timing) and obtain the IP address (it is a limitation of the Tor model: Tor preserves anonymity only as long as the relays are much more numerous than what the attackers may muster).
Once the police forces know the public WiFi from which the data upload began, they just have to have a look at the recordings from the security cameras, and then see your face. You'd better wear a fake beard (possibly over your genuine beard, if you have one). Also, the WiFi access points will probably record your MAC address, which reveals the brand of the hardware and can be compared with that of your laptop, should you be intercepted at the airport (MAC addresses can be changed programmatically, but you have to think about doing it).
Undercover upload without detection from police forces which are known to be, let's say, "proactive", is a difficult task. In particular, legalistic protection of the type "they cannot prove anything against me" will not be sufficient: you don't want them to suspect anything about you. This is a use case, even the use case, for steganography: you'll want to embed the litigious files into innocent-looking data. For instance, first get a bunch of pictures of cute kittens. Then, use a steganography tool to hide the data in the pictures. Once outside of the country, extract the files again, and do the upload from a presumably "safe place" (e.g. from a public WiFi hotspot in a country which is known not to collaborate with Chinese political police).
This still has the problem of getting the tool itself into the country in the first place. Having that on your computer or a USB key could be incriminating. Downloading it from elsewhere once you are in China is also subject to tracking. You might want to learn the source code by heart, and type it in on a brand new laptop which you buy there (and discard after the steganography tool has been applied).
You would still have the problem of file comparison: if you use public photographs of kittens from the Internet, then the police forces could download the same pictures, and see that yours do not match, bit-to-bit, the ones which are publicly available. Instead, make 3000 photos of your own cat with your own camera, and don't publish them on the Internet. (Side effect: the Chinese police will think that you are worshipping your pet to utterly unhealthy levels.)
