Make sure you get the right connector for the Genesis end. The Genesis 1 and Genesis 2 have totally different connectors.
Here's a site that has pinouts for both versions: Genesis AV.
Your projection TV actually is a CRT at its core. It uses a super-bright, smaller CRT that is focused and reflected through a prismatic mirror system similar to the top part of an overhead transparency projector.
They're different types of shooters. Ikaruga is more like a manic/bullet hell shooter than RS is. The polarity element of Ikaruga is absolutely brilliant.