I have a page where I list websites similar to mine in a "links" page. There are a lot of outbound links on that page. If I disable that page from being indexed, will I get into some kind of suspicious trouble with google? Its the only page where I have outbound links and I don't want to seem shady; I just don't want it indexed.
You can exclude any page from being indexed. It is generally not an issue or a red flag to search engines when done in moderation.
Having outbound links is not necessarily a bad thing. Some would even argue having zero outbound links is suspicious. Don't worry about it or lose sleep over it.
I have never known a search engine to ban a site because it has too many or too few outbound links. I do know of search engines not indexing individual pages that it deemed to be low in value because the individual page had only 1000 links and no text. I doubt that is your situation.
For my sins I am volunteer webmaster for a regional arts organisation. I run not one but 3 links pages giving directories of organisations, businesses and performers in our region. They are all indexed, they don't seem to do any harm and we get quite a few "drive by" hits where the linked sites are low in the SERPS. A proportion of those may click our Google ads or buy items from our on-line shop so I don't begrudge the others the tiny amount of bandwidth that they consume.