The solution depends on how the hyperlinks are created. There are two ways to generate a hyperlink in Calc:
- Menu
Insert -> Hyperlink
- using the
HYPERLINK() function.
In the first case, LO Calc inserts a field.
In the second case, the result is "plain text" with additional functionality if the user clicks on the hyperlink text.
Formatting a "text hyperlink"
Formatting a "text hyperlink" (created using the HYPERLINK() function) works the same way as formatting any other text content: using direct formatting - applying text style properties directly using the toolbar or Menu Format -> Text; or using cell styles.

Formatting a "field hyperlink"
Formatting a "field hyperlink" (created using Menu Insert -> Hyperlink) is somewhat more complicated, but it has the advantage that LO will apply a certain styling by default:
The actual design of "field hyperlinks" in Calc is the result of two settings: Field shading, and link color. You can't set the link color on a per-document basis, instead changes are applied application-wide (will affect hyperlinks in writer, too).
LibreOffice <= 5.0.x.x:
To modify the "field hyperlink" link color (and in calc, the link background -> field shading):
Menu Tools -> Options -> LibreOffice -> Appearance. Search for "unvisited links" or "visited links", and change the color:

For the field background in Calc, scroll down to the Text Document section (!), and change the "field shadings" setting.
LibreOffice >= 5.1.x.x:
To modify the link color (and in calc, the link background -> field shading):
Menu Tools -> Options -> LibreOffice -> Application Colors. Search for "Unvisited links" or "Visited links", and change the color:

For the field background in Calc, scroll down to the Text Document section (!), and change the "Field Shadings" setting.
Important:
Take care to tick the checkboxes at the left of the setting name (in the second screenshot: marked with red rectangle).
Important, too:
Don't apply magenta to hyperlinks, as in the second screenshoot - looks extremely ugly...
(LO 5.1.x: Tested with both Linux x86_64 and Windows 10)