was planning on a group tour to Elsinore, Kronborg and Fredericksborg, but I leave Copenhagen the day before the tour season starts. Other ways to do this on public transport or tour?

Rent a car, you’ll accomplish more and save time by doing so or take the train to these places.

Thanks but no interest in renting a car. Can I do this easily via train?

Looks like Louisana museum might be on the way to/from Helsingor?

It is. Kronborg Castle is in Helsingoer and walking distance from the station. You can use www.rejseplanen.dk to figure out public transport. I always drive as the route north of Copenhagen is scenic along the coast and is more convenient for me than public transport.

Looks like this option could let me do it off-season:

Grand Day Trip around Copenhagen | Hamlet Tours

I easily did in one day Frederiksborg Castle and Hamlet's Castle in Helsingor - by train so so easy. For train info check: https://www.dsb.dk/en/ (Danish Railways); www.seat61.com and for where to go in Denmark by them: BETS-European Rail Experts and www.ricksteves.com. There used to be at least some kind of day ticket good for S-Tog (commuter) trains all over eastern Denmark.

Louisiana is near a train station just south of Helsingor - so easy stop but probably not also with the two castle towns.

I went from Frederiksborg to Gillelje - nice fishing village selling fresh fried fish on beach and then the neat Gillelje Bahn along wild cost to Helsingor. Lovely lovely ride. Takes little extra but something few tourists do.

You should get the 24-hr all zone ticket for this trip. Can be done in one day, but I did them in two separate days because I also visited the Louisiana Museum (so I paid for 2 separate 24hr tickets). See map above to see the rail lines.

Another place to consider hitting coming back by train from Helsingor is on edge of Copenhagen - Baaken - world's oldest amusement park - and similar to Tivoli with lots of free entertainment and charged for ride.

Meant to add Bakken is right near a train station.

Bakken: https://www.google.com/search?q=Bakk...w=1745&bih=863