At present, there is no option to switch off the tcp time-stamp for to-the-box ASA https traffic.
1) The ASA does NOT include a Timestamp option for SSH traffic.
2) The ASA DOES include a Timestamp option for HTTPs traffic (this is be design).
3) The ASA does NOT initialize the counter to zero at boot time, but uses a
random value between reload/reboot (also by design).
Hence, while indeed the ASA includes a TCP Timestamp option on HTTPs traffic, that option cannot be used to determine device uptime. And no, a tcp-map will not clear the Timestamp option being added to traffic generated by the ASA itself.
If you are concerned about TCP Timestamps traversing the ASA - then it would be best to add a tcp-map to your global policy using the clear option. The following article shows how to perform this task easily. http://secureitnetworks.net/index.php/2015/08/21/how-to-remove-tcp-time-stamp-from-packets-on-cisco-asa/
Once you have the tcp-map in place, use the sho service-policy command to show the timestamps cleared.
EXAMPLE:
ciscoasa# sho service-policy
Global policy:
Service-policy: global_policy
Class-map: timestamp_class_map
Set connection policy: drop 0
Set connection advanced-options: timestamp_tcp_map
Retransmission drops: 0 TCP checksum drops : 0
Exceeded MSS drops : 0 SYN with data drops: 0
Invalid ACK drops : 0 SYN-ACK with data drops: 0
Out-of-order (OoO) packets : 0 OoO no buffer drops: 0
OoO buffer timeout drops : 0 SEQ past window drops: 0
Reserved bit cleared: 0 Reserved bit drops : 0
IP TTL modified : 0 Urgent flag cleared: 0
Window varied resets: 0
TCP-options:
Selective ACK cleared: 0 Timestamp cleared : 6763
Window scale cleared : 0
Other options cleared: 0
Other options drops: 0
