Can I disassemble my Chinook Anti shock hiking pole

Almost certainly not. None of the hiking poles listed on Chinook's official website list "disassemble-able" as a feature (nor any variation thereon).

I have a similar pole of a different brand. Like the Chinook poles, mine has three collapsible/expandable sections, with an internal spring for shock absorption. It does not disassemble, in fact it has warnings on the sections at the point where you should not pull them out any further. I suspect that due to the internal spring, disassembling would result in parts flying everywhere, and the entire thing would not be re-assemble-able.

However, I have traveled with this hiking pole, including bringing it on an airplane. I packed it at the bottom of a duffel bag, and there were no issues. I did factor in the possibility of having my hiking pole confiscated by TSA when I packed it. At a ~$20 pricepoint, potentially losing it to airport security seemed like a reasonable risk to me.

If not having your hiking pole would completely ruin your vacation, I suggest investing in a collapsible hiking pole. There are many options available.