For small races like you have, many years ago, we'd hand out index cards as they finished with race finish number pre-written on them. Finishers would write their name/age/gender on the card and put them in the assigned box of their age group, where you can add their official time later. If you did this for the first 50 or so, that would probably cover 90% of yur age group winners (how deep in age groups would you go ?).
You could still pull their bib tags and "string" them as backup and for finding winners in the remaining slower age groups. Your local sporting goods store probably has a fish stringer which always worked great for us. Make sure to string all tags face down as they go on. One person pulling the tags at the end of the chute, another person placing them on the stringer in order.
If your race gets bigger, it'll probably be worth it to contact a reputable timing company (local if possible). They'll have software which can quickly spit out results in a standard format, and their service might save you headaches that you wouldn't believe.
Good luck.