No, you CANNOT USE Hall of Famers. All Hall of Famers are banned in this league. But I think that is just a typo and you meant to say you can't use HOFers.
If you look under the awards button on the player profile, HOF is listed under awards.
Players that are NOT HOF members but did win the MVP, Cy Young, Rookie of the Year, Gold Glove, Reliever of the Year or were on the All-Star team some seasons ARE eligible in the seasons that they did not win any awards.
Just set the Draft Center drop down menu for "awards" to No Awards for each search of a player, and you will not have any problems.
The only three players that are not easily excluded by that simple move are Ted Simmons, Derek Jeter and Larry Walker, because they ARE HOFers but the WIS database won't include them until the currently postponed due to Covid initiation ceremony (or whatever its called). But they are also out.
Any player other than those three that shows up if you do a search for "No Awards" will be fine. Dave Parker was not MVP every season nor even an All-Star every year. So he should have seasons where he is eligible. Even Barry Bonds and Roger Clemens have years when they are eligible, Pete Rose too. Other seasons, when they were All Stars, or winners of other awards, they are excluded. The search engine takes care of it when set on "No Awards".