Bicycle Mechanics - 6 speed to 9 speed conversion

I am going to convert my 6 speed to be a 9 speed. I know I will need to replace the freewheel to a 9 speed cassette (I have a new wheel), shifters and chain. I am also replacing the rear derailleur. I thought I once read that the crankset will need to be replaced also, because of the spacing between the chain rings will allow the 9 speed chain to fall between the rings. I have seen a lot of info about upgrading, but I haven't seen the need to replace the crankset. I don't know if I thought I read that once or not. Does anyone know if I will need to replace it? The crankset now is a Sakae CR.

You don't need to replace your crankset, and most likely the RD either.
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You will probably have to respace the frame dropouts from 126 to 130 mm or plan on fighting the rear wheel on every wheel change.

Yes, I know about going to 130mm spacing, Thanks though. The RD is going to be changed because I couldn't find anything about Shimano shifters with Suntour Cyclone 7000 compatibility. Though the Suntour is working great when I am in 6 speed index or 8 gear friction. I just decided I want to upgrade this bike to a 9 speed with Shimano barcons, I thought I would need a Shimano RD, because I want index shifting. I will save the Suntour for another bike.

Good to know about the crankset. I guess I was imagining about the chain falling between the rings.

By the way, I assume I will eventually need new rings when these wear out. I tried a search to find new rings for this crankset, but could not find any. So, I guess I will need to go to another system eventually. Will I be able to just find a crankset that matches the spindle or can I find a spindle to a newer system that fits with the BB or will I need to get a new BB also?

The reason I am asking is because I am thinking about going to a compact double and was wondering about the BB/crankset compatibility.