There is some weak evidence that high intake of fish high in omega-3 fatty acids EPA and DHA (salmon, mackerel, roe, anchovies, tuna, herring, sablefish, sardines) or fish oil capsules might delay wound healing.
Here is one experiment about wound healing in rats fed with fish oil:
Detrimental effects of an omega-3 fatty acid-enriched diet on wound healing (Journal of Parenteral and Enteral Nutrition, 1993):
The omega-3 fatty acids contained in fish oils have anti-inflammatory
effects with potential beneficial clinical applications. However,
these same effects may alter wound healing, a process dependent upon
an adequate inflammatory response...At 30 days, however, wounds
harvested from rats fed the menhaden oil diet were significantly
weaker than those from corn oil-fed animals... Dietary consumption
of a diet rich in omega-3 fatty acids may conspire against the quality
of wounds by altering the fibroplastic or maturational phases of the
Here is one review article about post-operative wound healing in humans Role of Arginine and Omega-3 Fatty Acids in Wound Healing and Infection (Advances in Wound Care, 2014), which says:
Omega-3 fatty acids from fish oil can prevent wound infections and can
improve early wound healing, but after several days may decrease the
deposition of collagen, possibly preventing extensive scarring.
So, according to this source, fish oil may delay wound healing, but prevent scaring, which could, at the end, be a beneficial effect.
ω-3 fatty acids effect on wound healing (Journal of Wound Repair and Regeneration, 2008):
The results presented in this paper linked the EPA/DHA dietary
supplements...and nonsignificantly slower wound healing.
Omega-3 Fatty Acids Modulate Wound Healing (Advances in Wound Care, 2011):
Dietary supplementation with ω-3 fatty acids affects the local
production of cytokines that mediate inflammation in wound healing
processes. Further research is needed to determine if this effect is
ultimately beneficial or detrimental to wound healing.
The article linked from the question does not mention wound healing, but that histamine in fish can cause "allergies."
It is known that histamine can build up in non-fresh or improperly stored fish and cause scombroid poisoning with symptoms similar to food alllergies: flushing, itch, hives, diarrhea...but I havent found any association between scombroid poisioning and impaired wound healing. Concluding from this study in mice, histamine could actually promote wound healing.