I believe this is a very nice initiative to think and work towards reducing the stray dogs/monkeys menace from residential areas. This problem has been there for quite a long time and not much have been done by concerned authorities. I would suggest a couple of things:
1.) Not sure if civic agencies have sufficient funds so no harm in getting help from some NGO or volunteers who can help financially. I believe RWAs can also pool in some funds if they are assured that they would get rid of the problem.
2.) Hire/employ some experts who can capture the animals.
3.) Tie up with some veterinary doctor in case immediate need arise.
4.) Get assistance from civic agencies to find an appropriate place to serve as next habitat for animals.
5.) Last but most important : Form a governing body(of volunteers) to oversee the progress and manage. May be people from each part of the city can join in. I believe some of the elderly people who have rich managing experience under their belts would suit best.