Vouching for you was acceptable in Slovakia/Czechia in past, but it seems they removed it in recent years since I can't find any information about it, but I clearly remember if election commitee member could confirm your identity or 1-2 other people they could let you vote even without any ID card.

Btw. there is really no registration in Czechia/Slovakia, you will get voting tickets automatically to your permanent residence address without any additional registration, registration is necessary only if you want vote via mail or you want voting pass to vote outside your permanent residence.