Is there a way to delete a single message from an MQ queue (arbitrary position in the queue)?

a) You can use the MQ utility "dmpmqmsg" for a message in a specific position. Attribute: -r position

 For the specific scenario of deleting the 1st message in a queue, see the following article:

https://www.ibm.com/support/pages/node/7148300
Using IBM MQ dmpmqmsg to delete only the first message from a queue

An example to delete the 1st message from queue Q1 and create an output file with the contents of that message (in the format used by dmpmqmsg) is:
  dmpmqmsg -m QM93WIN -I Q1 -r 1 -f deleted-message-1.txt

An example to MOVE the 1st message from Q1 to Q2 is:
  dmpmqmsg -m QM93WIN -I Q1 -o Q2 -r 1
 

b) You can use the MQ utility "dmpmqmsg" based on a MessageID. Attribute: -gxm MessageID

For example, via MQ Explorer or amqsbcg you see that the MessageId for the desired message that you want to delete is:
 

414D5120514D393357494E2020202020F4C0F96501AB0240

Then the following command will do a Destructive Get (effectively a Delete) and store the message in an output file specified by -f:

dmpmqmsg -m QM -IQ1 -gxm414D5120514D393357494E2020202020F4C0F96501AB0240 -f out.txt

c) One method to delete a single message is by using the following SupportPac in an MQ Explorer in Windows or in Linux x86 that can remotely connect to the queue manager in AIX.
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The following SupportPac MS0P has the feature "Message Manager" that can be used to delete a message, to copy/move it to another queue, or copy it into a file
Download the zip file, and from the pdf file see: Message Manager Plug-in, Page 28
https://www.ibm.com/support/pages/node/712469
MS0P: WebSphere MQ Explorer – Extended Management Plug-ins and Tools
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WebSphere MQ Explorer plug-in for Events and Statistics reports

Plug-ins
• The original plug-in written for this SupportPac provides a mechanism to format Event messages; it can aggregate the Statistics and Accounting reports generated by MQ from Version 6 onwards.
• There is a plug-in to display current activity on queues and channels as a simple graph.
• The package also implements the "Trace Route" function, reporting on the route that messages take through a network.
• A plug-in to allow information shown in many of the Explorer’s tables, such as the list of queues defined on a queue manager, to be saved to a CSV (comma-separated value) file where it can be processed by programs such as spreadsheets.
• *** Another plug-in extends the Message Browser, to allow messages to be deleted, moved to another queue, or written to a file. ***
• A Wizard makes it simple to define connections between two queue managers.
• The topic objects defined on a queue manager can be displayed in a tree structure, to make it easier to see the relationships between them.
• Queue Manager configurations can be extracted using the dmpmqcfg command. This is accessible via the Remote Admin plug-in for queue managers at V7.1 or later, or via the main list of queue managers in the Explorer tree, if the dmpmqcfg command is part of that Explorer installation.