Replacing analog scope BNC input connectors
There is nothing inherently unsafe about what you're proposing. The only significant safety risk associated with this undertaking is the presence of a CRT and potentially large capacitors. Please note that standard cautions apply regarding these and you should look up informative instructions in advance of attempting your modification. A few points though from a practical standpoint rather than safety:


The BNC connectors on the scope are normal but I am assuming they have broken or something and this is driving your desire to replace them.
There may be an implication for signal quality with whatever you replace them with (stick with shielded cables if possible). Recalibrate the scope if possible (usually a clip on the front).
Cable stress.
Assembly/disassembly difficulty.
Don't break anything because you may not be able to find parts easily.


If you are still uncomfortable with the concept, imagine you are repairing the connections on the back of a TV--what would you be worried about there? The answer is a CRT and large capacitors (the same stuff). And someone in the room juggling hammers, burning yourself with a soldering iron, etc.