The least resource demanding method I can think of is to use cURL.
The code snippet below will broadcast using https://blockchain.info/pushtx
curl -X POST -d tx='your raw transaction in hex format' https://blockchain.info/pushtx
Example usage:
curl -X POST -d tx=0100000001492d631b86db96ab8b2d50bea0bec53ebde8eda603bdae6441289de454f89cd8010000006b483045022100e21e298f1ce99ade77502955b2bfa1acf1ada40a30e7b3a8ed86ae08bf9b7566022001a9b43a24abdb1b90eac434619f0a49ca2c8ec4152576ac8df0b63de43e2e68012102ed8725a530d72af0cbbaa96b1936042952ae73b78221edc596ea53c9a1c7a2b2ffffffff0210270000000000001976a914a0e6ca5444e4d8b7c80f70237f332320387f18c788ac250e0000000000001976a914ff4b370002146338c95827273de755e0eb8574cb88ac00000000 https://blockchain.info/pushtx
Otherwise I would recommend using a SPV wallet like Electrum, it is both lightweight and not resource-demanding at all.
If you are looking for the highest level of granularity/control, Bitcoins the hard way: Using the raw Bitcoin protocol might interest you.