Electronics Repair Questions? Ask an Electronics Technician
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You should be able to, yes. Would you consider sending it to Garmin for repair?
If so, be sure to get all personal data off it, synced to a computer or similarly. They might reset it and wipe the data off in the course of the repair, possibly.
To help you decide whether to go with Garmin for the repair, see this page:
which can tell you what the flat-rate price would be for your Approach S-1 watch. (The page tells me that the flat-rate for an Approach S-1 is $79.)