Running bitcoin core in a low storage system
You cannot skip downloading the blockchain, but you can skip storing it.

If you run Bitcoin Core with the -prune=N or put prune=N in the bitcoin.conf file, only at most N megabytes worth of blocks will be stored on disk. N has to be at least 550 currently.

Pruning does not reduce the validation or security at all, but does prevent your node from serving historical blocks to other peers.