Negative interest rates will instead force big business to seek safe returns wherever they can - and that will not be by investing in small business. That money may well be deployed in competition against small business.
Consider this... the US Small Business Administration's loan portfolio is barely a rounding error compared to the cost of quantitative easing and national security expenditures these past years. Double or triple SBA loans and USGOV balance sheet will not feel it, but the impact on job creation, salaries and investment could well exceed any benefit in the US from negative interest rates.