So with the recent spike in BTC price (and other ALT coins) when is a good time to sell?
As usual when you are in profit, but make sure not to be greedy and be realistic in your selling price goal. There are lots of people who got burned and end up waiting for another cycle because they got too greedy and hold their stash instead of selling them for profit.
Also is it worth selling the BTC shares and then rebuying when it dips again?
The spike of BTC price will probably continue until next year, when it reaches its cycle price peak. I don't see anything wrong on taking profit and rebuying when Bitcoin dips but be cautious about the timing since the timing determines how much your profit will be.