Are conventional and sustainable cryptocurrencies effective hedging instruments for high cryptocurrency uncertainty? This paper examines co-movements between conventional (Bitcoin, Ethereum, Binance Coin, Tether) and sustainable (Cardano, Powerledger, Stellar, Ripple) cryptocurrencies and two cryptocurrency uncertainty indices (UCRY price and UCRY policy). Using weekly returns from 1 October 2017 to 30 March 2021, the paper employs the bivariate wavelet coherence method considering three investment horizons, short-term, medium-term, and long-term. The results confirm that conventional and sustainable cryptocurrencies show consistent positive and identical co-movements with both cryptocurrency uncertainty indices at the short-term horizon during COVID-19 and negative co-movement at the medium-term investment horizon, suggesting the short-term hedging ability of dirty/green cryptocurrencies for high UCRY price and policy. Evidence of negative coherences shows that higher cryptocurrency prices and policy uncertainties lead to lower cryptocurrency returns, reflecting the adverse impact of higher uncertainties on the trust of crypto traders and investors. Weak co-movement is found between dirty/green cryptocurrencies and UCRY price/policy indices, which suggests the possible role of dirty/green cryptocurrencies as a weak hedge for UCRY price and policy indices. These findings provide potential avenues to hedge cryptocurrency uncertainties using conventional and sustainable cryptocurrencies across multiple investment horizons.