If I were to profit off cryptocurrency to cryptocurrency trades throughout the year without ever cashing out my crypto position for USD, would I avoid paying any short-term capital gains taxes on all of my crypto to crypto trades? Would I ultimately only pay long-term capital gains tax once I convert my crypto to USD after the one year mark?
It will depend on the tax laws in your country.
Where I live the tax law treats crypto currencies as an asset and requires that my position be reconciled at the end of each financial year for capital gains calculations.
That's not to say I have to do any buy or sells of each year I just have to determine my paper capital gain or loss for the year in order to include it on my tax return.