"my question is can i enable ip routing while the switch is running. will i cause any network issues?"
Maybe none, or in the blink-of-an-eye (i.e. impact [drops, delays] to inflight traffic), or long term (e.g. moving from default-gate to default-route).
Anytime you even "manage" access the box, adds some additional risk of something "bad" happening.
Worst (or best) example: Years ago I was working in a shop that had four L3 switch cores (non-Cisco, but equivalent to 6509s). All four cores, same exact models, same exact cards, same exact IOS, same exact power, same exact everything. However, one of the four cores was "hands-off" except during scheduled maintenance because just logging onto that particular device, or doing the simplest "show anything" might (and often would) cause that core device to hard crash. When left alone, it operated flawlessly. Other 3 core devices, you could logon, show this, show that, make some simple changes, no problems at all.
