Easiest way would be to simple import the addresses into Electrum. It's an SPV (light-weight) wallet with no need for blockchain downloads.

1. Go to Bitcoin.org and select "choose wallet"
2. Click Electrum from the list and follow the installation instructions.
3. When you start Electrum choose to start a new wallet (default, hit next)
4. Choose "Import Bitcoin Address" then hit next
5. Hit the folder icon in the bottom of the import window and import the file containing the thousands of addresses.

Since you are only dealing with public addresses you don't need to worry. To future readers... always be cautious of downloading wallet SW. It is a primary target for those looking to defraud you. There are some browser plug-ins that can help and some good common sense. Just be cautious.