35C means that the discharge rate can be upto 35 times the Ah capacity figure. There is no
promise at all that the cell capacity won't be vastly diminished, and it likely will be significantly
diminished at that rate, and the number of charge/discharge cycles will also be reduced by such
heavy use.
If the capacity is 0.3Ah, and 35C is given, that's simply a shorthand for saying the max discharge
current is 10.5A. If you exceed this discharge rate a fire may be caused, note, its wise to be
conservative about maximum ratings with LiPo batteries unless you are prepared for such
eventualities.
By the way you'll probably need to give up on at one of "small", "safe" and "cheap" - no battery chemistry
is ideal.