Kia Ora P-addy there are surf resorts in New Guinea and New Ireland. Surfing at them is very good in their season which is roughly November to March but more sketchy at either end of that period.
Madang and Vanimo are on the north coast of Papua New Guinea and the resorts of Rubio's Plantation and Nusa Island Kavieng are on New Ireland both areas are accessible by flights from Moresby. Surfing is very well controlled in New Guinea and numbers are limited as the New Guineans try and avoid becoming another Bali. There are also charters but you'd have to look at the sites selling them. All surfers at surfing resorts also pay a fee to help advance New Guinea surfing and aid the villages where they surf.
So there are no feral trips possible and you are right traveling alone is not a good idea, it is easy to make mistakes that offend local custom and tribal law
Now about Port Moresby, not entirely safe, I'm serious here,there are groups who want pay back on any white man worse than the Mongrel Mob (Hey I' m assuming Pakeha but I think they'd treat Maori the same) Anyway most companies who employ non locals have a set of safety protocols and social behaviours they coach you in. Safe pubs etc, if you have a girlfriend or partner going risk is higher.
At the resort areas you are safe, the local villagers are very friendly and there is not the problem. Just common sense and human respect. Learning Bislama (pigeon English) helps.BTW TAKE ANTIMALARIALS
see your doctor before you go I almost died of Falciparum Malaria years ago.
Final word could be an astoundingly different and great surf trip, serious preparation needed
I've taken up troll hunting just for fun, instead of a rifle I'll just use a pun!