Traditionally business houses or small companies had been raising funds through investors or banks or Govt loans but your requirement is to get funds from some other sources and not from these conventional ones.
So, There are some unconventional sources which one can try to raise funds for working of one's company and one of the main is Angel funding. But you have to approach them with some attractive start up plan. Which means that your business model should make them interesting to participate in it. These Angel investors are cash rich people who have a inclination to help and nurture the start ups in any area. There are many NGOs also who are coordinating with these Angel investors and are working as a liaison between the two the start up and the Angel investor. These Angel investors will monitor your business whether you are going in the same direction of innovation and business modelling as was envisaged during the funding phase. You may be surprised to know that some of todays big business houses like Yahoo, Alibaba, and Google were once funded by Angel investors only. There is a network of these Angel investors in our country and you can find more information about them in the relevant websites like https://www.indianangelnetwork.com and many others.
Another option is Venture Capital. Although this option is for slightly big companies but if there is a good potential in a business, they may like to review even the small set ups also. The advantage with venture funds is that they have a large experience in business arena and they guide the whole business and ask you to take corrective actions wherever you fail to steer the activities. They have access to the best experts in the field of investing and proliferating a business and are a valuable resource in all respect.
Another way which is slightly new and unique is that there are some contests held by some reputed agencies where one can submit one's business model and project and if one wins in these contests there will be many agencies to fund the project as they feel that it is well assessed by the experts and has immense potential for growth. Some of these main contests programs being executed in our country are NASSCOM's 10000 startups, Microsoft BizSparks, Conquest, NextBigIdea Contest, and Lets Ignite.
The most common and popular Govt loan scheme MUDRA loan is also a good choice but I am not elaborating on it much as you have excluded it in your query but still I feel it is worth to be considered.
For raising small funds for a limited time credit card itself is a good technique where one can have margin of 45 days for repayment without interest. Some entrepreneurs go for product pre-sale to generate small funds. Then there is another way that is to sell some fixed asset in hand which is not being used presently and from the capital acquired, run the business and later when conditions are conducive, acquire that or some other asset accordingly. Many businessmen do such things frequently.
Knowledge is power.