Hi Otto,This would probably be better off on the Arms & armour section of FireStryker, regardless, I'll give it a go here.
Historically, bascinets did not have catches, they usually would only have the visor lowered for a cavalry charge with the visor being raised after first contact, or lowered in an arrow storm. To stay alive in a battle you have to breathe freely and have good vision, and there are plenty of historical examples of knights and lords being killed because they left their visors up even in the most dangerous of circumstances.
In modern re-enactment as we understand the term on this board, there is nor reason to have the visor secured down in an inauthentic manner. Nearly all re-enactment (not martial sport) societies do not target the head, or if they do so do not allow foining toward the face, but a vertical blow at the crown of the head. We do not give and take blows at near full force (nor do any martial sport societies, or there would be no calibration - you would just hit each other as hard as possible), and so the equipment in it's original form (if not composition T.P.) is adequate for the purpose of safety.
A general rule of thumb in a lot of re-enactment societies is they do not allow the targeting of unarmoured portions of a person - this tends to cut down on injuries as well. Of course you must abide by the rules of the game that you play. A well hidden spring pin would be less noisome in my eyes than a whopping leather strap. Both are inauthentic for the 14th c.
Hope this helps
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Bob R.