Dynamic mics like the Shure SM58 are really good at rejecting (i.e. cancelling out) noise from behind the mic. They are used extensively by singers at concerts who need to hear their backing music using loud monitors positioned in front of them - a sound which needs to be cancelled from their own vocal feed and the mic is actually designed to do exactly this. These mics are also known for their resilience in harsh environments. So point the mics away from the main background noise source and get them close to the speakers mouths. When using a dynamic mic, instruct the speakers to talk directly into the TOP END of the mic i.e. speaking down into length of the mic. Especially, they must NOT hold it vertically in front of their face and talk to the side of it, as many are prone to do if they have used condenser style mics in the past or seen sports commentators using condenser mics on TV, or they risk sending most of their voice into the 'back' of the mic and getting it cancelled out!). Don't get mics with a switch, its just another weak connection point and prone to get turned off accidentally or introduce static 'hiss'.
For a quick easy setup in quieter environments, check out the ZOOM q2n webcam, which has pretty good quality stereo crossover mics, so you get video AND stereo sound from one source. The stereo recording will separate the speakers voices and make ambient noise / applause sound truly 'live'.