This is the bike?

Challenger SX & Mixte SX

It's worth fixing up. Downtube shifters are the cheapest/easiest assuming that the cable stops don't get in the way of the shifters; otherwise go with bar end shifters. You're best bet for finding vintage shifters are either a bike co-op or the C&V for sale section. Just put up a WTB ad. I just bought a set of suntour ratcheting bar end shifters. Those are great shifters and they'll do the job for you without having to modify the frame.

Some of the modern bar end indexing shifters have a friction option and will work as well but they will generally be more expensive than vintage bar end shifters. Be careful because some modern indexing bar end shifters do not have a friction option.

Friction bar end shifters are still being made. The dia compe bar end shifters are very good but not cheap at $56:

https://www.newegg.com/Product/Product.aspx?Item=9SIA4M57EG4763&ignorebbr=1&nm_mc=KNC-GoogleMKP-PC&cm_mmc=KNC-GoogleMKP-PC-_-pla-_-Cycle+Parts-_-9SIA4M57EG4763&gclid=CjwKCAjwjZjZBRAZEiwAPeLSKy6z_xawqb3zBLyROpIQQ9u3sXJe6Es7DhtNEs9XzudZ9jX2fGZG8ho C_vAQAvD_BwE&gclsrc=aw.ds

They'll do the job. I've used them extensively on a vintage touring bike that I ride and they're very good.