You could create a new datasource based on the old with only the name as the difference, and then point all the reports to the new one.

First, create the data source on the Reports website. The rest is done in SSMS

-- Step 1. Get the itemID of the current datasource

select *

from catalog

where name like 'oldDataSourceName%'

-- Step 2. Get the itemId of the new datasource

select *

from catalog

where name like 'newDataSourceName%'

-- Step 3. View all items linked to current data source (just to see how many rows you expect to update

--and verify that there are actually reports using the data source)

Select c.name, ds.itemid, ds.Link

from datasource ds

join catalog c on ds.itemid = c.itemid

where link = 'Copy Item Id from step one here'

-- Step 4. Update link to new datasource

update datasource

set link = 'Copy Item Id from step two here' -- new datasource ItemId

where link = 'Copy Item Id from step one here' -- current datasource ItemId

Test reports, then see if there are any items depending on the old datasource before deleting it.