There is a block-level parameter that allows the reset to be disabled on a block by block basis. You can access this parameter by right-clicking on a Delay block and choosing HDL Code -> HDL Block Properties. On this dialog, change ResetType from 'default' to 'none'. This sets the register generated from that Delay block to be generated with no reset.
The ResetType block parameter chooses whether a block will generate a reset or not. 'None' will not generate a reset; 'default' will generate whatever sort of reset is configured for HDL Coder in its Global Settings Configuration Parameters pane.
Since you have stated that you want the default to be no reset, the GUI-based interactive approach will be tedious. To script this, you can use the hdlset_param command, which has the syntax:
hdlset_param(block, parameter, value)
You can combine this with find_system to set all the Delay blocks in your model to have no reset:
hdlset_param(find_system('modelname', 'BlockType', 'Delay'), 'ResetType', 'none')
This will change the value of the HDL block parameter on all Delay blocks in your model to 'none'. Block parameters are persistent and are saved in the model, so this should be a one-time configuration. You can then go back and re-add a reset to those Delay blocks that require it.