My SSD space near depleted, blockchain 238GB

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If I use Exodus wallet address, will it work? I just worried if I block the newly generated block will not be recognize as spendable.
It will but I recommend staying with your own node instead. Simply change to a pruned node to save space. There is no need to keep the full blockchain if you have limited space.
Add something like this to our bitcoin.conf:
prune=10000
And that will limit it to using only 10GB of space. The lowest you can set it to is 550 which means only 550MB.