I'm going to use manufacturing costs as a proxy for environmental footprint. This is realistic up to the point that ignores extrinsic costs, and ignores financial costs. E.g. making the paper can be done with essentially no carbon foot print, or a fairly large one. In general I regard costs as being a good first order proxy, unless you can show some unusual circumstances.
The bitcoin calculations have to be redone on a transactional basis. Suppose that this was cheap and only took a kWh of electricity. Then the cost per transaction, ignoring equipment would be on the close order of 10 cents.
A debit card transaction typically costs the merchant 15 to 35 cents. The biggest part of this is to the company that runs the database. The non-material costs are a large fraction of this. (Where my proxy breaks down...) E.g. Database, data centre, are all manufactures that need to be amortized over all the transacations, but advertising, marketing both to customers and to merchants, dispute handling. I will arbitrarily call the cost of this transaction 1/2 of the merchant fee at 10-20 cents.
Credit cards, for reasons I don't know, are much more expensive for the merchant. Partly fraud, partly borrowed money, mostly making credit card companies wealthy. There is no intrinsic reason for it to be different from debit card. This difference is another example of monetary cost not being a good proxy for footprint.
While a dollar bill costs money to make, it will be used in hundreds of transactions before being retired as worn out. And a 20 dollar bill costs about the same as a one dollar bill to make. (The Fed's website says 5 to 20 cents for a paper bill. The $50 is the most expensive to produce.)
Bills last 5-20 years, with higher denominations lasting longer, as they are often used to 'store' value.
Figure that a bill on the average is taken out of a bank machine, and likely spent within two weeks. The shop keeper deposits it. So there is two transactions. Buyer to shop keeper, shopkeeper to bank. If it's a smaller bill, it has about a 50% chance of being used for making change, I'm guessing. So call it 5 transactions per month. 5 years then means a bill is used in about 300 transactions. This is a sloppy estimate. Could be as low as 100. Might be as much as a thousand.
Coins often cost more to make than their face value (especially true for small value coins) but a coin will be used for thousands of transactions. The penny costs 1.6 c to make, the nickle 8.5 c, according to an article in the washingtoon post. The others cost less to make than their face value.
According to the Royal Mint, british coins have an average life span of 40 years. No details about how they got this figure. In particular I don't know if they correct for the increased number of coins in circulation.